Never been on Jeopardy! but I am familiar with their tryout process.
First stage is a 100-question written test of general knowledge. Pass that and you go to the next stage, which is a mock Jeopardy game. Pass that and then that puts you in the contestant pool. You will have to travel to LA for the game -- the show does not pay expenses. (It's rare for Jeopardy! to do traveling shows, unlike Wheel of Fortune).
Five days' worth of games are filmed on one day; there may be times where you will wind up waiting in the 'green room' until you're called.
Couple of books highly recommended if you want to prepare for Jeopardy! -- here they are:
Secrets of the Jeopardy Champions
by Chuck Forrest, Mark Lowenthal (Contributor)
http://www.amazon.com/exec/obidos/tg...books&n=507846
How to Get on Jeopardy!... and Win: Valuable Information from a Champion by Michael Dupee
http://www.amazon.com/exec/obidos/tg...roduct-details
Looks like the second book's out of print, but with a decent search you can find it MUCH cheaper. Check out the reviews from a couple of former contestants there.
Good luck!
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