There were 9 of us, you can play with more. 8 sit in a circle, one was the Mayor (the referee). We all close our eyes ("go to sleep") and the Mayor walks around the room and touches 2 or 3 to be "the Mafia" (we had 2). Generally, a quarter to a third of all the players should be Mafia.
So after the people are picked, only the Mafia open their eyes and through hand signals etc. identify themselves to each other. When this is done, the Mayor instructs everyone to go back to sleep. Then he instructs everyone to wake up and everyone opens their eyes and the game begins.
The first stage of the game is called "Day". During the day, through discussion, argument and ultimately open voting, the Townspeople (including the Mafia!) must choose someone from their midst to eject, under the hope that the ejected person is Mafia. The Mayor does NOT indicate if their target is "guilty" or not, it remains a mystery until the end of the game.
The next stage is "Night". During the night everyone goes to sleep (closes their eyes), and then the Mafia awake and (through hand signals again) decide which of the townspeople to kill. That person is then removed from the game.
This continues, Day, Night, Day, Night until either the Townspeople win (by correctly selecting and ejecting all the Mafia) or the Mafia win (by "killing off" everyone else). If there are an equal number of Mafia and regular Townspeople, the Mafia automatically wins.
The Mayor needs to be careful to instruct the Mafia to go back to sleep before asking everyone else to awaken. Otherwise, people can tell who already had their eyes open at daybreak.
I was a regular townsperson. On Day 1, we elected to kill off an innocent person (whom we didn't know was innocent) on the grounds that someone felt the table shake and it could have been one of a few people, so we just chose one. Then the Mafia killed off a townsperson on Night 1.
On Day 2, we were busy accusing each other of being the Mafia and I caught on to one guy who said, "you guys are worse than the Mafia!" HMMM... "YOU GUYS", huh?!?! I challenged him and got him ousted. That very night, I got killed. =D It turns out I was right, he was Mafia. I was too smart for the other Mafia person so she off'ed me in the night. =)
That was a really nifty game.