See the block of text from the original page for more info on these.
At any time, the game is either in one of two states (night and day), or in transition between these two states (dawn and dusk).
The order always follows the natural order (dawn -> day -> dusk -> night (-> dawn etc.)), but the starting time depends on the game type, usually starting at night.
This might be useful/relevant/etc., but isn't necessarily what we'll be following. A quote from Methew:
When you want to vote, clearly state what you are doing with your vote by capitalising it such as VOTE DASQUIAN or UNVOTE. It is normal to put this in a chat explaining why you're voting this way, otherwise you tend to look suspicious. You may retract or change your vote however much you want before a majority is reached.
The moderator will, throughout the game, post updated vote counts and remind people how many votes are needed for a lynch (it will be a strict majority, so if there are 20 people alive, 11 are needed to lynch). Once the majority is reached, it's twilight and that person's fate is sealed. Votes may be removed and readded, but it won't make any difference, that person's going to get lynched. You may still chat until the moderator announces that it is night.
You may also vote for "NO LYNCH". Voting for no lynch is similar to voting for another player - the difference is that if "no lynch" wins the vote, the day ends as per usual but nobody gets lynched. Simple eh?
It cannot be stressed enough that it is strictly against the game rules to talk about the game with other players off the channel (night-communication roles notwithstanding). I just want to take a brief moment to underline why this is so.
The core mechanic of Mafia that the game revolves around is in deciding who to trust and who not to trust, based solely on what you see on the channel.
In this light, discussing the game outside of the channel raises problems. Even an innocent discussion about how you hope you don't get lynched, or that you're confused about how the mafia does their stuff, inevitably means other players listening use what you say to make up their mind about whether you are bluffing or not. Of course, this disadvantages the players who aren't there, and it means the discussion isn't logged to be referred to later like the main channel.
I know that this has caught me and other players off-guard in games I've played in, so this is a note to say how far it's acceptable to push the IC/OOC boundaries by invoking the influence of the moderator. The answer is: all the way.
Nothing a player says within in the context of the game is required to be honest or truthful. For example, it's entirely fair, if a little sneaky, to feign some sort of private dispute with the moderator to throw a cloud of confusion over your otherwise shoddy defence. A case in point - I've played in a game where a mafia member told the town he had posted something he shouldn't have about his role, but that the moderator had seen it and deleted the post. This was a complete lie, but most people assumed it had to be true and hence he was innocent, because a post that they hadn't seen had allegedly been deleted by the moderator! Of course, the moderator kept a stony silence...
So it's important to realise that within the game itself, only the moderator is a reliable source of information - the moderator will neither confirm nor deny rumours about his/her behaviour or private communication to players.