I'm a new DM and wanted to make my own campaign. I had an idea of what I wanted but no clue where to start. So I first started my party off with the Lost Mines of Phandelver and introduced small parts of my own campaign so that the switch over made sense. But now we have like half a session left of what I have from the book and I'm panicking. They're currently in wave Echo cave and have to beat the black spider. During the fight, he is going to try and destroy the room. He's going to open a portal to his world and their only option is to follow him through it (if they let him survive) or be crushed by the mountain. His home world is on the border of the plane of air and the material plane made of floating islands and continents.  When they make it through the portal they are just gonna be in a small clearing and after a while if they don't start adventuring on their own I'm going to have an owlbear start chasing them to the edge of the island where they're going to realize they aren't in their world anymore. Other than finding travel, I'm not sure what to have them do first. 

EDIT:

Thank you for all of the guidance! It all really helped! I dont think I gave enough details in my first post but I do have an intention for them to be in this world. I have made sure with everyone having very simple backgrounds that there aren't any ties to Faerun. I have an intended end goal for the players but was stuck on what should be done next when they arrive to get them acclimated. I'm going to have there be hints of what to do while they are doing these things and then encourage them to investigate their new world further. The plan is that the magic of the world is starting to fade and smaller islands are beginning to fall. When they come through the portal and do a bit of traveling to get their bearings they're going to learn about the most recent island having fallen when they had come through the portal. They are going to be tracked by government officials because they exude a different wave of energy which was sensed when the portal was opened and taken to the council where they'll be asked for help since everyone's worried that magic is becoming unreliable. In the end, it is going to turn out that one of the council members and their followers are behind all of it and has a syphon tower so that they can conduct a spell they made to gain godlike powers so that they can enter the the material realm and take over. While speaking with the council, it will be explained to get back to their world they need to find the cosmologist because there is little research done on planar travel other than by his group which he is one of the last and traveling looking for a worthy apprentices. It is going to turn out that the black spider was sent to their world by the cosmologist to find any other possible additions from other realms. 

First thing first what is the idea behind your campaign?

Going from LMoP to full on homebrew campaign can be a big swing and a lot of work so you need to be prepared for that.

ultimately I would say you don’t need to be a whole campaign ahead of your players you just need to be 3-4 sessions ahead of them. However if you are nearing the end of campaign material and now getting worried about not actually having content then you might need to take a step back and ask why you are going off piste in the first place.

I have been doing a 2 session weekly game of my own campaign since quarantine began that started with sourcebook adventures before becoming my own campaign just as you described above. So that’s about 6hrs of content a week I have to plan, which in turn takes about 12-15 hours from idle thought to execution. It’s not easy but I find it rewarding enough that I have started a second campaign doing just that all over again. If that doesn’t sound like what you think you are signing up for by going in your own direction and that panics you, maybe use some of the resources on DM’s Guild, here and DrivethroughRPG to get sone adventure modules to place in the world.

i am not trying to be mean but it sounds like you have put a lot of thought into flavouring how they are getting to your world abd it’s geography to ground it, but not very much into why they are there and what they will do if you have so far is “I guess an owlbear could chase them”.

If you are a new DM that is creating their own world I am going to go out on a limb and say that it was live play streams that got you here. Which are all unique homebrew worlds to invest their viewers and it gives the impression that is the only true way of playing D&D.

1) those streams are often made up of players and DM’s with a decade of experience, whose job is often to be creative

2) Sourcebook adventures exist for a reason.

I can agree with sardonicmonkey, you need to think about

- the overall campaign goal (what is the rough direction of your campaign climax) or do you just want a sandbox (which is ultra tough for a beginner DM).
- what is the rough plot to get then to the campaign climax
- plot hooks, what are the options to the players to actually go and do something, and how do you communicate these options within the game
- short story arcs that advance your story, and what has to happen within these arcs to get the campaign going forward

In your example you first want the PCs to explore and have their own motivation of 'getting back home' after realizing they are somewhere else now. Easy way here, is to make the earth mote, they are on small enough to realize their situation fast enough. After that, you need a plan to motivate them to leave the floating mote of earth. Maybe they see a larger mote with a city not too far away.

Then, how can they get away, plan the encounters they can have to get off the earth mote.

When they are off and away, what next, what will they find, who will they meet, what will happen, that pulls them into your planned story?

And on and on and on. You do not have to prepare everything in one go, but only for 2-3 sessions ahead, always keeping your overall goal in mind.

"if they don't start adventuring on their own I'm going to have an owlbear start chasing them"

What you are going to have there is a group of people fighting an owlbear... It can be hard using creatures to push people along as they will always have a tendency to just fight it.

I've also about to start running my own homebrew campaign. I have been planning it in for about 2 months, and even still only have first 6 sessions with an ideal of the overall plot arc. I have also been running some homebrew oneshots based in the same setting. This has helped refine my planning as the first one I ended up scripting the whole thing, where as now I do more note form which I find better. 

So, the first question that popped into my mind is unfortunately a 20/20 hindsight question, which is that if you wanted to do a homebrew world, why didn't you just located Phandelver in your world, rather than starting the characters off in Faerun and having them switch worlds?

Have you really thought about the consequences of complete, and from your description irreversible, world-switching? Literally everything they know and love will be gone for them. Their families, friends, etc. -- all they will have left is their party. Everything in their background will become nearly irrelevant. That guild that your rogue said was hunting him for stealing a valuable item - gone. The fighter's ex-girlfriend from the tavern - gone. Are you prepared to have them RP the kind of PTSD that would logically result from losing their entire world forever? Watch Season 1 of the Supergirl TV show to see her reactions to this -- and she has had 12 years or so on earth to come to grips with it. Are you going to give them 12 years to get used to the new world? Or do you want to have RP session after RP session with them RPing their characters being sad, depressed, lonely, etc? Because that is the logical reaction someone would have to ending up in a totally alien world with no way to get back home to the people they love and the things which are familiar to them.

Therefore, my question would be, how invested are your players and their characters right now, in Faerun? Are they locked in? Or can you say that all the locations you mentioned in the module so far are locations in your world, not Faerun? And just draw the rest of your world around that region? Use the names from the module but everything else outside this area is homebrew. Would that throw everything off-kilter -- and more to the point, would it throw everything more off-kilter than what I just described above in terms of how one would logically RP the world-switching?

If you have no way of gracefully doing this without the "world-switching" then I would recommend instead, considering that this LMOP module was a "one-shot" in Faerun, and then starting new characters in your homebrew world. This is an alternate world so tell them, if they really like the PC they are playing, they can make up the alternate-earth version of that character and just keep playing him (kind of like comic-books, how there used to be a Superman on Earth-1, and a Superman on Earth-2, and they are very similar in many ways but different in a few details). You could even start them at a higher level if they don't want to be level 1 again. But make it clear this is an alternate world, and they will need to write up a background that covers the first 3 or however many levels, as well as whatever they wrote before. In other words, "Your characters did not go to Phandelver, etc., because it does not exist on this world so let's make up what they did do instead." Or, you could play that out, if they want.

I think your players will be much more on board with this kind of thing than with you just zapping their characters to another world, no way back, and "you're here now, suck it up." 

I don’t think world switching is necessarily a problem, but ultimately players need context and motivation. You don’t need a sweeping, world changing campaign, but you do need to engage your players’ interests for at least a few sessions to feel out where their interests lay.

The best advice I ever got as a DM was to create a situation where you don’t have specific expectations of the party. Understand your NPC’s key motivations. Then throw your players into the mix.

You are either going to need something to engage their interest on the other side or you are going to have to give them a motivation to try and get back. In both cases it needs to be pretty clear what their options are. There is nothing worse than being in a situation where the players have no idea what their options are and you are putting it all on them. 

A couple of ideas:

- drop them a few clues that hint at how they’d return (ingredients, maybe the text of the incantation to open the rift, leftover scroll, maybe something dropped during RP by the black spider).

- maybe have something on the other side encouraging them to work with the black spider to return/survive. Bad guy becomes reluctant ally. 

- they step through into a battle/argument/execution/trial/ mugging/lair/prison cell. It could be something which they have no cultural context for which might be fun for them to fumble through.

- there are transdimensional bounty hunters that chase those that cross the dimensions. There were chasing down the black spider, now they are chasing the party as well.

- put them on a clock. they feel the foreign plane begin to drain their life force. Insert mechanics here. 

Whatever you want, but don’t think about steering the party. Think about giving them raw material and let them run with it. 

Oh, and steal. Maybe you just rip stories and plot from Sliders or Time Bandits. 

Of course, another option would be to simply end this first adventure and start anew in your world setting with a new group of adventurers. Alot of the fun of playing D&D is thinking of new characters (for players) and seeing them grow in their environment. This way you won't force anything and the players can consider what they wish to do. They may like their character types alot and redo a similar character or try something different. 

I would recommand having a discussion as a group and decide together what's next. The session 0 is always a great help in starting something new (which sounds like what you want to achieve) and then as a group find the proper answer for your party. 

Remember, even though you are the DM, the story is a group effort and by collaboration do you ever get the best results.

Yup, definitely include the players on your plan. Don't worry about "spoilers" - for something like this, you need to make sure they will like it. You don't have to tell them the specifics of the spider but you should say something like, "Now that we all want to keep playing, I'd rather make up my own homebrew world than use forgotten realms. Is it OK with you guys if I alter the ending of this adventure to teleport your characters to another world? Or would you rather start over with new PCs? What do you think?" See what they say. I mean they might love it in which case the first time you show them a portal they will leap through it on their own because they know what you are doing.

You can do almost anything if the players are on board. Matt Colville has a great example of this with his first episode of the Chain of Acheron. In that episode, one player, Lars, had his character basically one-shot-killed in a battle that was clearly too powerful for the party. A lot of viewers objected to this in the stream chat and said this was unfair to Lars and so on. Colville later explained, he had given his players a choice of 4 campaigns, and one option was to play the Chain and to start out with the "fall of the Chain," basically, their final, failed mission under the old commander, and then the campaign would be about fleeing that city and going somewhere else to lick their wounds and rebuild the chain. They had all chosen to do this -- they knew they were going to be in a losing battle on the first session and that one of them (but not which) was going to die. Out of all the options he gave them, they unanimously chose the one that guaranteed a losing battle in the first session. Lots of people watching, not realizing this, thought oh, that is a horrible way to start a campaign -- but the players loved it (Colville would later say that they couldn't stop talking about it the whole next week and thought it was awesome). And Lars stepped into Colville's discord to say yes, he knew his or one of the other players' characters would probably be the one to die. They expected it -- no, WANTED it - that way.

Normally you would not kick off a campaign by overpowering the party and purposely beating them and killing one of them. Most players would not come back after a session like that. But if the players know what is going to happen (in a general way) and are on board with it, then it works -- and it was fun to watch (they recorded the session) and a cool opening, and they loved it.

So... do what Colville did. Talk to your players, and see if they are on board with switching worlds or what they would like to do. If you get player buy-in, you're golden. But if you don't get player buy-in and you just spring this on them, you may be in for a lot of trouble and possibly even people leaving the campaign. So make sure you get buy-in.

Thank you for the guidance! It all really helped! I have made sure with everyone having very simple backgrounds that there aren't any ties to Faerun. I have an intended end goal for the players but was stuck on what should be done next when they arrive to get them acclimated. I'm going to have there be hints of what to do while they are doing these things and then encourage them to investigate their new world further. The plan is that the magic of the world is starting to fade and smaller islands are beginning to fall. When they come through the portal and do a bit of traveling to get their bearings they're going to learn about the most recent island having fallen when they had come through the portal. They are going to be tracked by government officials because they exude a different wave of energy which was sensed when the portal was opened and taken to the council where they'll be asked for help since everyone's worried that magic is becoming unreliable. In the end, it is going to turn out that one of the council members and their followers are behind all of it and has a syphon tower so that they can conduct a spell they made to gain godlike powers. While speaking with the council, it will be explained to get back to their world they need to find the cosmologist because there is little research done on planar travel other than by his group which he is the last and traveling looking for a worthy apprentice.

Don't stress too hard about being too prepared.To appropriate an old adage: DM plans, players laugh. have a story arc in mind, prep a few key goals for each adventure session (things you want them to learn, things you want them to get, things you want them to fight), and let the players explore. Especially if you're doing a new world, your players are going to explore it in ways you didn't expect. If you try to prepare EVERYTHING, you're going to wear yourself out, and you won't be able to devote the attention you need to the campaign that's ACTUALLY being played.

Triggers are also a great tool. You can define them as you wish, be it time, location, action, and they start the next encounter you planned. It might not be necessary to wait for the players to do something very specific to go on, just throw the encountern in, where it fits. The players do not know and will not know, that your initial idea was, to have the encounter in a very specific environment. If you keep it vague for yourself, you can alter and apply your encounters much more flexible. 

Example: I used an encounter from the 4e DMG, where goblins attack a small town in order to steal back a magic totem from a small shop. The players were in town and were wandering around trying to figure some related business out. I let them go their own way and waited in that session patiently until they returned to the place where that shop was located and then triggered the encounter. They were involved without beeing railroaded, got hooked because the frigging greenskins tried to kill them on the way to the shop, but still got away with the item (which was one of the possibilities I prepared, the other being, that the players stopped the goblins from taking the item) and then worked from there. Works wonders if you do not plan on the players to do something in a specific order if the story needs to advance. 

Quote from Hevans5 >>

Thank you for the guidance! It all really helped! I have made sure with everyone having very simple backgrounds that there aren't any ties to Faerun. I have an intended end goal for the players but was stuck on what should be done next when they arrive to get them acclimated. I'm going to have there be hints of what to do while they are doing these things and then encourage them to investigate their new world further. The plan is that the magic of the world is starting to fade and smaller islands are beginning to fall. When they come through the portal and do a bit of traveling to get their bearings they're going to learn about the most recent island having fallen when they had come through the portal. They are going to be tracked by government officials because they exude a different wave of energy which was sensed when the portal was opened and taken to the council where they'll be asked for help since everyone's worried that magic is becoming unreliable. In the end, it is going to turn out that one of the council members and their followers are behind all of it and has a syphon tower so that they can conduct a spell they made to gain godlike powers. While speaking with the council, it will be explained to get back to their world they need to find the cosmologist because there is little research done on planar travel other than by his group which he is the last and traveling looking for a worthy apprentice.

 
As everyone is throwing around old adages I am going to go with “Show don’t tell”. Try having the players experience what’s happening rather than just learn about something.

have the first floating island they arrive on be a smaller one that at some point begins to fall, plan a set piece where they have to try and escape it, then have them witness the same thing happen to another nearby.

don’t explain it too soon, let them panic and jump to conclusions, it will definitely speed up their travel if they are unsure if the area they are in is going to stay afloat.

maybe have a sky ship on hand that can fly in and rescue them if they screw up but only use it if they get really unlucky and are unable to escape the sinking islands.