Congrats, man. I got to the audition for the college test a few years ago, but that was as far as I went. The biggest thing is to be loose. Dress nice, but don't get stiff or nervous. Start practicing the buzzer now, because they do make you play a fake game.
This afternoon, I just happened to run into the one person I know who has appeared on Jeopardy!, and he actually won two of the three nights one which he appeared.
1) Learn all of the state capitols. Learn as many country capitols as you can. Know your basic geography.
2) At least know the titles and authors of the major novels. There's a book that lists this that is in most major libraries, and, apparently, is a standard reference for most English and Literature graduate students.
3) Try to learn the major artistic (film, music and art) works.
4) He did say that most of the stuff he studied was never asked (or answered, as the case may be). But it was useful to get into that mindset, so it wasn't entirely a waste.
He did suggest a few other things, but I'm blanking on it. He's given me permission to forward you his email. PM me if you're interested. He's a real nice (and talkative) guy.
At the audition, you're going to be taking another 50 question test.
After that, assuming you pass, you'll play a mock version of the game so that the contestant coordinators can assess your personality and how comfortable you'll be at picking clues, answering clues, etc. They're going to ask you for five stories (which was the hardest part for me!), so be prepared for that. They'll also ask what you're going to do with the money should you win. Then you get your picture taken for your contestant file. After that, you're in the contestant pool and it's really out of your hands.
Things you really should know: State capitals, World capitals, US presidents and their order (VPs are less important) - know who died in office and how, and the assassin if applicable. Some of the plays of Shakespeare (they're probably not going to ask about "King John" or "Cymbeline", but know "Hamlet", "Othello", "Macbeth", "King Lear", etc.) British royalty (plus the wives of Henry VIII). All those classic novels. Composers.
There's plenty of one-off stuff, like "Russian Jewish painter" is always Marc Chagall, and "Finnish composer" is always Jan Sibelius. Robert Burns is the Scottish poet Jeopardy loves. Etc.
Sporcle.com is your best friend. There are quizzes for all these things.
The show loves to reuse categories. Watch the show (and go through the Archive - www.j-archive.com) and see what those are and look into what you're weak on in those areas. Watch the show every night and keep track of your score (the fan standard is the Coryat method - look it up on the Archive).
And the #1 thing you MUST know: HOW TO WAGER!!! Go to the Archive and play around with the wagering calculator. It will give you suggested wagers for any scenario you want. Know the 2/3 scenario. Know when to bet everything and when not to. Don't be afraid to be bold on DDs if you find them.
One thing I'd add, just as a longtime viewer: make sure you know the basics of Canada. They ask a lot about Canada, possibly because Trebek is from there. You don't need to be an expert, but a good knowledge of the basics, especially with regard to geography, seems to help.
Get control of the Vale, and use that as a base to eventually challenge for the Iron Throne, although maybe by controlling it rather than sitting on it (much as Tywin was just doing). And he can't have Cat, but he can have her daughter.