I'm lost already. Could you please repeat the directions.
In its simplest form, Mafia consists of two sides: the Mafia, and the Town. The Mafia's goal is to kill the innocents (town, townies), while the Town's goal is to kill the scum (Mafia, some third party factions).
At the beginning of the game, the Moderator will secretly send everyone their role. The Mafia will know each other, while (in the basic game) everyone else will only know their own role.
The game has two phases, the first of which is Day. During Day, the Town must choose someone to Lynch; they are trying to eliminate the Mafia, but the Mafia can lead them astray by casting suspicion elsewhere. Generally, players will vote for someone they think is Mafia (the Mafia will vote so that they seem to be doing this as well, and might even vote for each other to confuse the Town). Before start of the game, the Moderator will outline lynch conditions in the rules. My preference: The player with most votes at the end of Day phase gets lynched. An alternative is: When a player gets a majority of the votes, they are lynched. When a player is lynched, their role is revealed by the Moderator, and Night phase starts.
During the Night, the thread is locked and no one can talk publicly. The Mafia, however, can speak to each other privately to plot strategy and decide who to murder before the next Day begins. In this way, they can silence members of the Town who are threats to them. At the end of the Night, the murder is carried out and another Day begins. In effect, the Town gets to kill someone, and then the Mafia gets to kill someone.
The game alternates between Day and Night until either the Mafia are eliminated, or the Mafia have killed everyone else (or nothing can prevent the same).
There are third party factions also, such as serial killer (scum), survivor (neutral), or cult (scum) -- each of these have its own win condition. Serial killer wins when everybody else is dead (and they get to kill one player each Night). Survivor wins if game ends and they survived. Cult wins when all non-cult players are dead. Cult is started by a cult recruiter; cult recruiter visits a player during Night phase to recruit them into their cult. Recruited players usually lose their roles and become vanilla; some moderators may add a twist, letting them keep their roles for x-shot use (where x is usually 1 but can be any number).
Games can also have different themes based on movies, books, tv shows, games, etc. and some Moderators may introduce different mechanics into the game depending on their setup.