Find or create a very small dungeon, and run a one-on-one session with them to show them the ropes.
you don't want other players trying to talk over you to explain things
you don't want the noob to get distracted by other players
you don't want multiple people fast-forwarding through the game mechanics and confusing the noob before the noob's had a chance to understand each game mechanic at their own pace.
you don't want players telling the noob WRONG information, which then wastes your time to correct / clarify
EG: your noob finds a potion. Player X starts talking about how potions come in different varieties, then gets side-tracked talking about treasures, and before you know it they're going on about sentient swords and other crap that's way beyond the scope of just showing the noob the basic ropes.
EG: your noob wants to do something. You tell them to roll against a certain skill or something. Another player interjects and says "akthually" it should be against some other skill. Argument ensues. Noob is left wondering who to trust, but, more importantly, is left hanging, bored, while you folks hash your conflict out.
You might be able to find a pre-canned intro dungeon online. But, you can easily make your own.
Shouldn't be more than 3 or 4 rooms... like a small crypt or goblin/kobold cave
It can have an entrance, and rooms lined up to work their way through to an exit point, with each room introducing a new mechanic.. or just have a hall junction that branches to each room and player can explore as-they-see fit to learn about each mechanic (this might be better, so player learns they get to make choices, not just get railroaded by you forcing them down linear paths).
Not to be cliche, but give them a basic fighter to start with, so they can learn basics w/o getting overwhelmed by extra character details, like spells or sneaking / lockpicking.
It should cover the basics for D&D:
- how the DM describes an area, and asks what the player wants to do
- a small combat (probably 1-vs-1, like a small skeleton or goblin/kobold)
- a non-hostile NPC the player can chat with, possibly learning that different alignments mean characters act a bit differently, which may conflict with the PC's alignment / motives (maybe they free a prisoner stuck in the crypt/cave)
- finding loot, but tell them since the character is in hostile territory, they'll just bag it up for now and count it later at the inn so you can move on without going into that detail yet
- magic items & usage.. like a potion of healing they can drink and identify
- skill test.. like maybe a strength test to bash a door
- saving throw test (do they still do saving throws?) to avoid something, like a spring-loaded trap in a chest with a mild poison that hurts them (good time to use the potion of healing)
- maybe encumbrance if you use it (most games I've played, DM's ignored encumbrance unless players got really abusive, like trying to haul around canoes on their backs)
It should also cover the basics of the play-style you prefer players follow:
EG: when folks first get into D&D, they just think "kill all monsters". But, as we mature, we learn that not every monster is hostile. Some can be chatted with, and a fight can be avoided. Maybe even valuable info is learned by doing so. So, if you prefer players try to be non-violent first, then you could have an encounter with a goblin or something that teaches that. They could come across a goblin child, and choose to kill it or let it go or help it. Who knows. But, it lets the player know they have more options than just munchkin-style "kill all monsters and reap the eeps!"
If your campaign uses some special basic thing every character would know about.. it would be a good time to introduce it to the player.
EG: if you had a sci fi game where forcefields hurt people when they touched them, you could have a forcefield in the intro dungeon that the player could push a monster into for damage, thus the player learns how forcefields work.
Just very basic stuff that would need to know, so they don't make a stupid mistake at the very start of a real adventure with a real character.
At the end of the adventure, that's when you teach them about the wrap-up...
splitting loot... now's the time to count the coins, and divide the loot. Maybe they learned about the crypt/cave from an NPC that they agreed to split the take with. So, they learn about splitting loot with others.
experience ... you've tracked what they earned from "defeating" encounters (either by killing stuff or evading it or talking with it non-violently), and maybe they get an overall xp award for an adventure completion. It should be enough for them to go up a level, so you can then discuss how characters gain levels and can look at new skills and such.
downtime... old-school D&D that I played just have faux down-time the DM and players would just assume stuff got done in, but I hear new-school D&D actually organizes downtime better. You could have the player go over something they wanted the character to do in downtime.
Downtime might actually be a good thing to START the adventure with... by letting the player know their character has an adventure coming up, but has downtime to prepare for it. So, they can decide how to use some downtime actions, and depending on how they decide, it will impact how prepared they are. Do they want to go shop for a new weapon or shield? Do they want to buy a torch or rope? It can help them learn how to use downtime and also shopping.
This adventure shouldn't take more than an hour to run through, and shouldn't be all that confusing. EG: a 1v1 combat with a goblin can teach mechanics without over-whelming the noob.
But, at the end, they should have a good grasp on the basics, and can be ready to draw up their own character.. which you could walk them through to prep it for joining the other players during a regular session.