Mafia
Positions
There are four positions in the game of Mafia, though they are not necessarily filled by only four people. Anyone in the game who is not one of these four is a townsperson.
God
Also known as the moderator, God has all the power in the game, and is the only one who knows everything that's going on. He decides who the Mafia, detective, and doctor are (unless that's chosen by cards). He also tells everyone when to wake up and confirms who is dying/being accused/saved. When someone is killed off, God gets to have a little fun and make up how the person died, often gruesomely and in great detail. This God has no relation to the God of Blammo.
Mafia
The Mafia is often made up of three people. When they awake, they all agree (by pointing silently) on who their next victim is. During the discussion period, they are supposed to accuse others of being Mafia so their own are not killed off. However, sometimes a Mafia member will accuse another member, or support a townsperson's accusation. If the game reaches a point where only Mafia members are still alive, the Mafia wins.
Detective
The detective is a bit of a tricky position. When the detective awakes, he guesses who is part of the Mafia (again, pointing silently), and God lets him know if he is right, often by nodding or shaking their head. During the discussion, the detective tries to persuade the townspeople to kill off anyone who he knows is Mafia. Generally, the detective does not want to reveal himself, because if he does, it is almost certain death for him in the next round. However, the detective is allowed to reveal himself at any point during the game.
Doctor
The doctor is also referred to as the nurse or the angel. When the doctor wakes up, he silently points at the person he chooses to save. If he has chosen the person that the Mafia earlier chose to kill, the person does not die. However, if they choose someone else, the Mafia-chosen person does die. The person the doctor chose is not affected. A selfish doctor will often choose to save himself.
Playing the Game
God is first chosen, and is usually whoever started the game. Everyone except God then sits in a circle. The Mafia, detective, and doctor are then chosen, usually in one of two ways: by taps from God while everyone else has their eyes closed (one tap is a townsperson, two is a doctor, etc.), or by God dealing each person a card (queen is doctor, king is detective, aces are Mafia, all others are townspeople). The second way is more often used because it's more fair, but the first way is used if there are no cards available.
God then tells everyone to go to sleep (close their eyes), and has the Mafia wake up (open their eyes). The Mafia then choose someone to kill. They go to sleep, and the detective wakes up. He chooses someone to accuse, and then goes back to sleep. The doctor awakes, chooses someone to save, and goes to sleep. God watches all of this, and confirms (or doesn't) the detective's guess. No one else playing can see this.
God then has everyone wake up, and announces the death of whoever the Mafia chose (unless they were saved.) Then comes the discussion period. Everyone has a chance to throw accusations, and then they vote on who they think is Mafia. The person with the most votes is killed off as well. Depending on God, he reveals what the position of the person killed off was. Everyone then goes to sleep again, and the process is repeated.
After a person dies, they are not allowed to say anything or make any signs towards who the Mafia is. They are allowed to watch the waking up and sleeping of the different people. The game ends either when all the Mafia members are killed off, or when there are only Mafia members still alive.
Variations
The most common variation is the amount of Mafia members there are. This depends on the amount of people playing. There should usually be at least three townspeople, and at least one more townsperson than there are Mafia members. The usual number of Mafia is three. If there is a particularly small group, there may be no doctor. In a very large group, there is occasionally more than one detective or doctor. Like the Mafia, however, they must agree on who they are choosing.
There are also other games that go by this name that involve handshaking and winking. They are rarely (if ever) played at CTY, and not as much fun.