Well, first you have to have someone willing to be a moderator. Depending on how many people we have, we either have one or two mafiosos.
There are two periods that are repeated over and over until the end: day and night. It begins at night, when the mafia members each pick a person to kill, and PM the bosser person their choice. (The bosser person picks who's what in the first place).
The game then moves to the day period, with the bosser person saying who was killed. Everyone still alive tries to decide who is guilty of being the mafioso, and try to lynch them. Basically, the game is a study in psychology, to see who can make themselves appear believable to the rest of the forum.
In order to lynch someone, you need a simple majority of votes (i.e. if there are eight people, you need five to choose the same person to lynch someone.) After a person is dead, whether by mafioso or lynching, they are no longer allowed to post in the thread.
The goal is to get all the other people on the same page as you, and to agree with you.
In some versions, there are other rolls, like detectives etc., but to start with, I think (if people actually want to do this) that we should just do townies v. mafia.
I would be willing to be the boss person, to keep the game moving along, and because I've seen it happen before.
Also, there is no editing in the actual mafia thread, so that if you slip up, you're kind of out of luck and you have to cover your tracks.
On the other forum where we're playing, we also have an off-topic discussion thread, where we can go off on tangents about what people say etc.
Umm... yeah. Here's[1] the wikipedia link if I didn't explain it well (which I feel like I didn't. So follow the link and read.)
It's actually really fun to try and figure out what others are thinking. And being the Mafia goon is intense, because you have to figure out who might suspect you and stuff.
I really am kind of excited to play this on a forum where I actually kind of know the people. (The other forum I'm on has only been around for like a month, total, so no one really knows each other yet.)
[1]
http://en.wikipedia.org/wiki/Mafia_%28party_game%29