So, I guess I ended up becoming the DM for my mom and sister. Neither of them have any playing experience and I have no DM experience, but I kind of can't turn them down because I've been bugging my sister to play DnD for a while and now she's finally brave enough to do it and my mom rarely gets excited about anything but now she seems pretty interested in this. I threw together a really simple 45-minute campaign as a test run to see if they like playing enough and I like DMing enough to continue, and we're planning to play it as soon as they go over the new player guide.

Any advice so I don't totally mess this up? Anything I can do to help my family understand and enjoy the game?

Remember that things that are second nature to you as a player are foreign ideas to someone new. They may not think to search for treasure, or understand when they should stand and fight or when they should run away. 

Introduce ideas slowly and dont push at concepts that obviously make them uncomfortable (such as in depth social interactions and heavy roleplaying). The learning curve can be steep and they will have trouble retaining a lot of information all at once.

Offer suggestions for actions they can take and give at least some idea of potential outcomes. Again they likely don't really know what they can and should do.

Explain rules as often as they need and without any frustrations. It wont help to make anyone feel dumb.

I have taught D&D to a lot of new players including my sister, my aunt, my ex-wife, and my current wife. The only common element I have found in teaching,  is that patients and friendliness are the only sure way to bring a player back to the table.

Thank you so much!

Make it fun and let them do it their way,

I just started dragons of ice spire peak with my wife and daughter (neithger had played before) and on the first session my daughter started up a conversation with a trader for gear they needed. This happened just after they'd been to the inn for lunch and had a couple of wines to wash it down with, anyway she failed her persuasion check (breathe smelt of alcohol, or maybe spilt some on her top) so no matter what she said it came out as if she was drunk/smelling of alcohol. 30 mins later my daughters she's still laughing on the floor about it (she's underage and she can now tell everyone she had to many...... and she sure wanted to play again) 

So in session 2 they spent over an hour conversating with a Manticore trying to eat the midwife at Umbrage hill It got to the point where they've convinced it to help them in the final battle if the town helped it recover by feeding it every day  (as her Ranger doesn't want to hurt animals), my wife (Bard) spent 10 mins persuading the mayor to honour the deal they made for the town to feed the Manticore, otherwise the Dragon won't be the only thing the town will have to worry about. I also made a big song and dance over how the payments done for completing a quest, one gold piece at a time....   So in 2 hours they completed a quest against a serious opponent without even having to fight it. Laughing there way through the entire session. 

It was a fun time, their were a couple of times I had to push them in the right direction, but after just 2 sessions they've started to learn the basics, and both are happy to continue.  

NB: i kept the sessions to around 2 hours.

All the best.

This is the best advice I can give any new DM: Watch Me. 

IamSposta beat me to it ;) Excellent place to start.

A few bits of advice from me though:

• You're going to mess up, and that's OK! Trust me, no one has made it out of the gate with zero mistakes ( even if their mistake was not recognizing the 20+ other mistakes they were making ). Play, evaluate, learn, improve. That's how you do this :) No one expects that you learn 100% of the rules before you can play or DM - and to-be-honest the rules are sprawling and complex, so they're neither complete, nor free from contradictions.
• Never stop learning; never stop analyzing your game style and trying to improve it: It can be a big complex hobby, and the targets are all moving as your Player base changes, their tastes change, and your tastes change. Which leads to ...
• Listen to your Players, and ask them questions ( although don't be annoying and hound them about stuff because you're insecure about it ): All games differ, because no two groups of Players & DM are the same. Think about the things you like about the game. Learn what your Players like about the game. Build around that. If you do that, and do it well, everyone will have fun with it - which is the goal.
• Learn to Improvise, and keep polishing this skill: You will never ever ever ever learn to predict your Players perfectly - although with some experience with a group of Players, you'll be able to predict rough outlines to a pretty good degree of accuracy ( although never discount the perversity of Player whim! ). If you can roll with the punches, you can seamlessly and flawlessly keep going when ( and it's when ) your Players run off the material you've prepared into unknown territory. You will eventually find yourself improvising Characters, Plot Elements, even Mechanics!
• Lean on your Players: You don't need to do all the work alone! Have a Player track Initiative, have a Player keep track of Monster damage ( they are going to be doing this anyways - you might as well get benefit from it ), appoint one Player Party map-maker, appoint one Player "party caller", etc.
• Lean on your Players ( part 2 ): Players have creative input to the table. Don't be afraid to steal their ideas and run with them - although don't do that in the spur of the moment! Take those ideas away, and design around them, and polish the results so that you have well crafted and consistent results. If you just thing "yeah, we'll run with that!" you run a high risk of introducing inconsistencies and problems into your adventure that you didn't notice right away. Also - if your Players are heavy into RP ( not all are; that's OK as well ), they'll hand you things in their background or personalities that you can build facets of your adventures around; use them!
• Lean on other DMs: Read, watch, ask questions of other DMS. Beware that other DMs are stubborn opinionated sons( or daughters)-of-*****es. Review what the opinions are, and what the evidence is, and then make up your own mind.
• Understand the WHYs: Behind every mechanic, and every DM opinion, there is a purpose and a goal.  A DM might say " the way you do this is .... ", but what they really mean is " I value X in my game; this approach promotes X; therefore I like it". Which is fine. But if you don't value X, their advice isn't useful to you. The mechanics of the game emphasize particular game elements and style; maybe you want to alter that.  If you think about why things are done a certain way, and what the results are, you can mix-and-match in what promotes the kind of game you and your Players want - not what some opinionated jackass on the forums like me wants :)

I'm sure we can go on for days, but here's the most important one, IMHO.

Don't ask/think/analyze/design forever. You only ever really learn by doing. So - get out and run the game. That will teach you more than 1000s of forum posts ever could.

Best of luck :)

Great advice so far.

Adding a bit to what Vedex said,    "Learn to Improvise, and keep polishing this skill" 

Try to not detail every single point as if you are writing a novel,   you won't have that level of control -- your players collectively are more creative than you are.   Instead, have some higher level ideas and understand your villain and setting's motivations.  That way if the characters do something unexpected (normal) you can easily adapt  because you're not focused on the detail, just the objective and motivation.

You are going to be great, so don't stress. Remember the main point is to have fun, so make it more enjoyable for you and your players rather that worrying about being perfect. Its totally fine to mess up the rules. The players dont notice half the time anyways and just go with it. You only need to know the basics of the mechanics (how to attack, saves, skill checks, how to generally cast spells). But remember, rules are guidelines. You can houserule as needed. Here are some DM tips :

-like Lauren said above, have a Zero session. Go over expectations, setting, atmosphere, goals, backstory, anything you or your players think is relevant to your game. It can help ease you into the game.

-Dont stress about the story telling. You arent telling the story, the players are. You are just filling in the blanks and adding general guidance and atmosphere. Takes the pressure off of having to know everything.

-There is going to be dead noise when the players dont know what to do or to say. Its fine, not everyone is a professional actor or role player. Gently coax them and give them options, see what they can come up with.

-Only have the players roll if the outcome of what they are doing is uncertain. A character that jumps off a 300ft cliff will die. It doesnt matter that they rolled a 20 on their acrobatics skill check. Its common sense so there is no point having them roll for it. Same as, a king isnt going to give you his kingdom just because you rolled a 20 on a persuasion skill check.

-20 is only an automatic success (& critical) on an attack and a 1 is only an automatic failure on an attack. This isn't the case for saving throws and ability checks.

-Failing an ability check doesn't mean you didn't accomplish what you set out. It can also mean a complication or that it just takes longer than you expected. (ie: if your characters need to find a secret room to advance the adventure but fail their perception check, then your game isnt ruined. The fail can mean that they spent so long looking for the secret door that when they do discover it, they are also found out by a roaming patrol of orcs or it gave the gelatinous cube time to sneak up on them.) Failures can create opportunity for creativity and story.

-When describing something add descriptions that connect with the all the senses not just what they see. Its fine to say its a 20 by 20 stone room. Its more immersive to say its a 20 by 20 stone chamber, you hear a dripping noise from the far left corner. The flagstone crunches beneath your boots and there is an acrid smell to the air. Saying a dragon breathed a 40 foot cone of fire is fine. Saying you see the dragon take a deep breath and the sudden whiff of brimstone touches your nostrils feels more thematic.You dont have to do it for every single thing you describe but for exciting parts its more fun. Just go through what they can see, hear, feel, smell (or any combination you see fit) in your description.

Games give you a chance to excel, and if you're playing with good company you dont even mind if you lose because you had the enjoyment of the company during the course of the adventure. One of the best things I remember Gary Gygax quoted as saying was “The secret we should never let the gamemasters know is that they don't need any rules.” And you dont. You can play a whole game just through storytelling and imagination and have a great time. So if you can have a great game using "nothing" then imagine how easy it will be for you to have a great game with all the resources and rules already made for you. Have a blast.

P.S. - If you need help with general monster tactics and how to run them in combat you can message me as well and I'd be happy to break down any specific monster you have and how the monsters act in combat.