The ninety-second rule
If a new player is not doing something fun within ninety seconds of picking up a controller, you have picked the wrong game. That is the whole test. It rules out anything with a character creator, a settings walkthrough, a story cutscene, or a tutorial level - all of which are perfectly good things that a beginner experiences as a queue.
It is also why the free party games work so well as an introduction. Fall Guys puts you into an obstacle course immediately. Among Us gives you one job and a room full of people to be suspicious of. Neither asks you to learn anything before the fun starts.
What to actually say while you play
Three things help more than any game choice. First, do not explain the controls - hand them the controller and let them press things, then answer questions as they come. Second, never say "it's easy"; say what to press and when. Third, resist playing well. A group of experienced players sweating a match in front of a newcomer is the fastest way to end their interest, and it is entirely within your control.
If they are joining a group where everyone else is experienced, put them in co-op, not versus. In co-op their mistakes cost the team and the team laughs; in versus, their mistakes cost them personally and everyone watches. That is the difference between a good first evening and a last one.
The next step up
Once somebody is comfortable, the natural progressions are: Overcooked when they want something with real teamwork, Sackboy or Shredder's Revenge for a proper game with levels and a bit of challenge, and Stardew Valley or Minecraft for the person who has decided they like this and wants something to keep playing.
That progression can take a week or a year. The mistake is skipping it - buying somebody a premium co-op game because you love it, and watching it go unplayed. Our gift guide covers the same problem from the buying side.
Long-distance beginners
If the person you are trying to include is not in the room, phone games are even more important, because you cannot lean over and show them anything. Among Us over a voice call is the standard answer, and Jackbox works over a screen share. Games to play on a video call and free mobile games are the two pages to read next.
Kit and cost
The cheapest possible start is free: Among Us on a phone, or Fall Guys on a console somebody already owns. The best-value paid start is one Jackbox pack for a room, because it covers up to ten people from a single purchase - see games where only one person has to buy it.
If you are buying hardware into this, remember that local multiplayer means one controller per player, and consoles ship with one. Two extra controllers cost more than most of the games on this page. Live prices for every pick are in the table at the top.
The one-line answers
A room of adults, mixed experience: Jackbox. Four people, one Switch: Mario Kart 8 Deluxe. Someone who has literally never played: Nintendo Switch Sports. Over a call: Among Us. Free, tonight, anywhere: Fall Guys. Once they are hooked: Overcooked, then Minecraft.
Two adjacent pages. If the friend's hesitation is about the microphone rather than the game, games to play with friends without talking lists the ones with built-in pings and quick chat so nobody has to speak. And the Jackbox Party Pack review covers the lowest-friction option of all - one person owns it, everyone else joins from a phone with a room code and nothing to install.