It sounds complicated, but it is actually pretty straightforward (in execution) once you start playing. Basically, there are only 2 things that happen in every "round" of play...
1) All citizens (which is everyone) vote on who they THINK is a mafia member, and the person who gets the most votes is executed by the mob, and removed from the game. The moderator then informs the citizens whether or not the person they just killed was in the mafia.
2) The mafia, in secret, decide amongst themselves who they are going to "whack," and inform the moderator. The person who is whacked is also removed from the game.
Everything else happens sort of behind the scenes, and if you happen to get randomly selected to be a mafia member, a vigilante, or an informer, Chris would include your special instructions in the PM.