Two teams (usually...some variations). Mafia vs innos in a 1:3 or 1:4 ratio. Mafia can pm each other. Innos are usually standalone. Innos try to eliminate mafia during the day session; some discussion, everyone votes (mafia AND inno) and one person is "lynched" (voted out). After that person's role is revealed as mafia or innocent, the "specials" take a turn. Special innos have various powers - to "instakill" (one time kill of another player), to "investigate" (ask the mayor what a certain player's role is), or to save (protect themselves from the mafia hit, or protect another player from a mafia hit). Mafia gets one hit (kill)...they try to kill innos (special innos if they guess right). All of these are done by pm'ing the mayor (the game manager), who then announces them during the "night" session. Each morning, repeat - until one team eliminates the other.
Best way to learn it is to just "dive in" and play. Some of the longtime players are VERY good at the game, but having new blood really helps keep the game fresh because noobs can be unpredictable.