The easiest way to learn is to play it. It's really complicated to explain. Jorick did a great job of explaining it before the site crashed. If only we still had it. =/

The very basic gist is that each person is assigned a role with a certain ability. The players form a group (we will say a town). Terror strikes this down when one of them is killed unexpectedly. Using various clues in the story post, the town must figure out who is with them and against them. If the town kills the killer, they win. If the killer kills the majority of the town, they win. It goes about in phases. 

The Night Phase is for those with special roles (Killer, Doctor, Detective, etc.), This is when they PM the GM what they plan to do.
The Day Phase is one for contemplation and lynching. All players will vote to lynch one person. That phase ends when there are enough votes to lynch someone.

I am awful bad at explaining things, but that is a very quick write-up of how it works. If you both have individual questions, I can help you out. Rabbit Doubt is a game of paranoia, alliances, and strategy.