I’m relatively new to D&D and I’ve got a great group of players but I’m about to do a really big adventure and I’m not sure they’ll take it seriously. Any tips?

How well do you know the players in your party? Whatever tone you set in the first session is going to set everyone's expectations for the rest of the adventure. That isn't to say the tone cannot change, but it's an important first impression. I'd just be honest with the players and tell them what you hope to get out of the adventure and then listen to what they hope to get out of it as well.

Being a DM is a vulnerable position :)

My best recommendation for you is to have a session 0. This is a session where you can have all of your players together, and you can pitch them the tone of the campaign and what you expect, and hear from them what they want. This is also a great way for the party to build their characters together and flesh out interparty relationships if any of them know each other from the start. 

Thanks, man. this really helps. :)

Even if you are confused, make it seem like everything's under control and make stuff up if you have to.

Don't let your players push you around, but be flexible and understanding.

If your players argue, remind them that all their skills are needed/wanted/useful to complete the campaign.

If there is a rules argument between dm and a player, I usually allow one or two back and forth statements for them to convince me.( "but what about this rule", or "doesn't this impact the situation") if they convince me I adjust my ruling, if not I tell them this is my ruling in the moment and offer to discuss my handling of simmilar situations going forward after the days session.

Plan and prepare as much material as you can, even if you don't end up using 90% of it. Give the players reasons to jump through your story hoops. Be generous about rewarding them, but don't make it seem too easy. Give the players what they want, but make them play the game before they can get it. Also, remember what Gary Gygax once said: "The only reason the DM rolls dice is for the sound they make on the table."

awesome!

Hi. I just started that big adventure today and all the advice really helped, only, they decided to go to another direction which I hadn't planned and I managed to improvise just enough to get to the end of the session. I'm not sure what to do next.

Curious minds want to know: what's the story about, what did they do that was surprising? Otherwise I'm confident you can repuporse a lot of events/encounters in your next session you had originally planned in the first session (as long as it makes sense, players won't know better). 

I see you’ve learnt one of the first rules of dm’ing: no plan survives contact with players. In other words, you always have to assume whatever you plan will break down, that the players will do something you don’t expect.

now, as for help, you’re going to have let us in on where the situation is at and what the plan was.

as a start work out how to get them to go in the way you want them to, the simplest method of doing this is to write them into being members of an organisation and send them on a mission to start with. winging it becomes easier as you go along but it just makes your life too difficult to start with as there's so much to remember.
the thing to do now is make notes of what you created on the fly or anything that's likely to come up again so it stays consistent. inn keepers look the same act the same and have the same name for example.

then you could work out a few clues to send them back down your original direction. or simply go with it and prepare some more.

another  method is to have set scenarios that advance the main campaign theme, but not to have them in a set place, then you can drop it in somewhere suitable. use those to grab your parties attention and get them interested in their enemies, so it only matters that it happens and your party sees it, not where, though it does help if it offends your group of characters in some manner. 
you can prepare some quite detailed material that way and the only pieces you need in a set location are the big setpiece endgame encounters though even that location can be held as a secret to be discovered late on in proceedings. that allows you chance to devise something underhand devious and horrible, then drop the info when they can hack it 
you can also fling in little side quests complete detours and little gems as you get the inspiration,

drop them a map with writing on the back that they cant read. there's 3 quests there.
one to find out who might know how to read it, another to find the person who can read it and the last to act on what they find out.
while they're off investigating the map drop in the after effects of your big baddies having done stuff, a burning farm house attracts attention from a fair distance particularly from local watch and adventuring parties. don't let the watch arrive till after your party have though, then you can have the watch looking for your party because they're the ones suspected of burning it down. all your party find at the burning farm house is a dead orc outside and a burning building but no sign of any other people. (you know personally that the orcs are working for your big baddie, collecting people for use as slaves) but they might not become interested till you've burned down your 5th farm house or more. because they have the map to keep them occupied now.

at the end of the map quests your party find something interesting by this point they've become annoyed at constantly finding burning farmhouses and decided to off and sort out the orcs, while your party is off sorting out the local orc problem, the interesting thing gets stolen from their base, because your big baddie needs it for his plans and he's had a minion hire some thieves to retrieve it for him,  this should annoy your players as they've just spent lots of effort finding this shiny thing. if you want to add annoyance, they could have left it with some form of sage who is trying to work out what exactly it was, the sage could then inform them that not only was it interesting it was something special but it's been nicked. 
things such as that will allow you to unfold a story centred round your party while they don't even know they're involved in something to start with and tootle off doing as they please

Something that i did to prepare for my first campaign is that i ran one of the prebuilt campaign released by WOTC. I did the "Tomb of Annihilation" which helped immensely with showing me what to plan for, how to prepare areas and NPC encounters, and how to pace and set a tone for the story. If you dont plan on going this route then i suggest reading the core rulebooks so that you can have a solid foundation of the rules and their applications. You dont need to have an encyclopedic knowledge of the rules but having an advanced understanding of how they work will give your players faith in your ability to run and lead the game. I also suggest evaluating how your players perceive or react to RPG games. I dont know how experienced you or your players are but lets say that imagining fights in their imagination will be confusing or cause issues later then i recommend using a battle mat to help orient the players with their position in the fight relative to the opponents. I chose to use the mat for fights where position can be important or where it can be complicated to keep track of all the creatures/players. Lastly you just need to make sure that before every session you are prepared for what you plan to have happen and possible routes your players can take. This will help prevent you from getting lost in the story and struggling to catch up to the players and build the world as they go. In the end the best way to draw your players in and engage them in the story is to be knowledgeable, prepared, and aware of how your players react to the game and plan from there. I hope this helps and i wish you luck with your game.  

I would prepare some random encounters and sort of smaller side-quests for if they go do something completely unexpected. You could also try having these encounters chain back to the main story in some way, although this depends on a lot of other factors. 

I also wouldnt assume what the players are going to do. They will surprise you from time to time. I personally just prepare the problem, the reaction to the most straightforward approach the players might take (I.E: If there are monsters, what happens if the players try to kill them immediately), and then improvise from there. 

Trying to have an idea for what will happen in the long term is tricky because its very easy for the party to 'derail' and do something differently. Just focus on giving things to the party on the short term that will bring them along  a general plot bit-by-bit.