It can take a lot of time, but it's fairly straight forward. There are 2 phases: day and night. A deadline is set for the day cycle and everybody has to vote to kill off one of the players in an attempt to find the 4-5 "mafia" in the group. During the night cycle the mafia get to select a player to kill off. Civilians win when there are no more mafia alive and mafia win when the number of remaining mafia equals the amount of civilians (since they would be able to control kill votes). You can just kind of half-ass pay attention to what people say or you can go over it with a comb.
The game is a lot of fun. I'm assure you that it is nowhere near as nerdy as joygasming over Greg Hardy retweeting you (though that is awesome).