That's a bit too broad a category of games to cover.
So I'd narrow things down to playing text based Mafia with the rules we use on this forum.
First of all, there are two main factions, Mafia and Town, the game is centered around the conflict of these two factions as they try to eliminate the opposing faction or hostile factions before they can be eliminated instead.
Additionally, there are players that have unique objectives that are either hostile to Town making them a Third Party or they aren't hostile making them a Neutral player. Town must eliminate all Mafia and Third Party Roles in game, or all Mafia Roles are eliminated and the Third Party Role or Roles completes their objective without all Town Roles dying.
During the game, there are two main phases, a day phase lasting for 48 hours and a night phase lasting for 24 hours. Each role has specific abilities and general actions they are allowed to use depending on what game phase it's currently on.
For the day phase, all players have the following action they use by posting in the game thread itself ##Vote <Insert Player Name here>, this is a vote to kill that player at the end of that day phase. It's majority rule, so usually each player's vote will count as one vote toward who will be lynched that day by everyone in game. In case of a tied or split vote between two or more options the GM will decide by random selection which option is going to be lynched that day. And as long as it's before hammer time which is one hour before the end of the day phase you are allowed to change your vote by targeting another player with the ##Vote action. Additionally, there is usually an option to ##Vote No Lynch, which means no one will be killed then at the end of that day phase by the lynch.
Also, depending on your role you might have day actions that allow you to carry out a unique action that can only be used during the day phase. Examples of actions might be a second vote, an ability to outright kill a player assuming they don't have a defensive ability known as BP or bullet protection, or even an ability to make you immune to being lynched. If you have an ability like this it'll be defined in your role PM as to what effect it has, and as long as it's not a passive ability then you must post ##<Action Name> <Target if Needed> in order to use that ability during the day phase.
For the night phase, night actions are carried out a bit differently, instead of posting them in the thread you will send a PM to the GM telling him what action you want to use and specifying who or what you want to use it on if it needs to be targeted. Night Actions are considered to be hidden actions as compared to Day Actions, so the GM will send you a PM telling you the result of your night action at the end of the Night Phase. One action that is almost always present in game is the Night Kill which is usually a factional kill ability reserved for the Mafia team in game to use, and as you'd expect allows them to stealthily kill a player during the night phase of their choice, assuming no other night actions interfere with it. Some night actions let you track or watch a player visiting another player, other actions prevent a player from dying, while still other can prevent a player from performing any night actions at all as they are blocked by another players night action for that night phase.
Now, other than actions the biggest part of the game is the communication aspect, in which you directly post in the thread, sharing information with other players, arguing with them about what happened, calling other players liars, and trying to defend yourself if someone accuses you of lying. Normally, you aren't limited in terms of how many times you can post during the day phase, but during the night phase you are limited to a total of two post in the game thread for that entire night phase.
Additionally, there are abilities in game that form a Masonry with a player. This is a unique action that let's two players communicate with each other in a private google document without the rest of the players in game knowing about their conversation. Mafia always have a factional Masonry in game, in addition to a NK ability which are the defining aspects of the Mafia faction, along with it's smaller player count as compared to Town. This forces Mafia to have to try and deceive Town into fighting among itself, while avoiding giving Town the ability to catch them and Lynch them during the Day Phase.
As for game setup, in a ten player game you have the following factional breakdown. 6 Town players, 2 Mafia members, and 1/2 Third Party/Neutral roles. As Town their biggest concern is trying to find out who Scum is in game. Scum is a catchall term for every player with a Mafia and Third Party role. Once Town finds Scum their job is to eliminate them through killing actions, which the most common one available to Town is by having enough players to have the majority of votes for the day lynch. That is also why Town generally loses the game if they fail to catch Scum before enough Town Players die that they lose control of the Day Vote majority. This generally translate over to about the third or fourth day phase the game will end with all Scum being eliminated or gaining control of the Day Vote so Town can no longer eliminate Scum from the game, and resulting in a Mafia victory.
