All there official rules for performing an Exorcism, or is it purely up to the GM? I haven't been able to find any; that's fine if I have to make it up myself, but I want to make sure I'm not just missing some actual rules first.

Hey!

Its in the Radical's handbook, right after Daemonic Possession. In the Elite Advances (Page 70-71).

Man, poor guy who has to go trough that

Edit- You gotta possess the guy, by summoning something (It refers you to the rules for chaos rituals on page 160), and then wrapping up that ritual will be up to the GM. Though, there's a number of faith talents in the inquisitor's handbook or more so in the Blood of Martyrs book that will take care of it relatively easily.