EDIT: This guide is a bit outdated, and the in-game one has been updated, but it's still a good introduction nonetheless.
I'm making this guide because, lets face it, the one in-game isn't worth squat.
Transformice is a game where you are a small mouse, like everyone else on the level. You will be automatically placed into a room with a number, but you can change to any room you want by typing "/room exampleroom" without the quotes, and put your room's name where exampleroom is. All commands in Transformice are used by writing / something. The rooms get created when someone types the name in, and are non-existant when no one is in them. A good room is room jig, or room TC. These are frequently empty, so have a backup. At this point all rooms are public to whoever knows the name. Therefore, for a private room, make up a name that no one will guess.
When you're in a room, you will spawn as a mouse.
You move with the arrow keys, and jump with the up arrow. There's a chat bar in the lower left corner, a list of users and their points in the middle, and on the lower left is a list of users that have cheese and their times. The point of the game is to get the cheese at all costs and then get back to the mouse hole. To do this, you may or may not need the shaman's help. Some levels are user created, in which case you will be expected to vote on how enjoyable the level was to play. I will write another guide on the special level types. Anyway, more guides are on the way, and if there's anything basic to add to this guide, or if it helped you, comment!
A mouse with circles of any color on it is called a shaman, who can call up items and save other mice. I will write a shamaning guide that explains this. Sometimes, shamans will "troll", by killing off mice. Don't get mad at them, they'll do it more. If it really bugs you, just leave.