How to Tryout
So you think you've got what it takes to become a contestant on Jeopardy!?. If you want the nitty gritty details, you should check out the official Jeopardy! web site or listen for information during the final commercial break. But here, I can give you some firsthand experiences on the matter. (I haven't appeared as a contestant, but I have tried out.)
First, all contestants are thoroughly screened for both knowledge and personality. You will have to pass an oral examination, where you are subjected to 50 clues in a variety of categories; and you should get at least 70% (35) of these right in order to qualify. (The difficulty of all these questions is about the same as the $800 or $1000 clues on the show, so scoring yourself on those clues should give you a good idea of how qualified you are.) The clues are presented in order, one at a time, with about 8 seconds to answer each one before moving on to the next. If you pass this, you'll then get to play a mock version of the game with others to show that you understand how the game works. (As you can imagine, the smartest person in the world that has never seen the show would not make a good contestant.) Finally, you'll get interviewed. If you pass all of these, you've got a good chance of making it onto the show.
If you're trying out as a regular season contestant, your name goes into a file, and when they need you, you'll get called. Don't be surprised if this takes up to a year or longer to happen. If you're trying out for one of the special tournaments (Teen or College), your chances are lower because only 15 people make it to the tournament each year. You'll have to try out year after year if you don't make it.
Jeopardy! looks for well-rounded, bright individuals that people will enjoy watching at home. If you come across in an annoying way, that isn't very enjoyable to watch. Trying too hard is probably a common mistake when trying out. Just be yourself; the contestant coordinators are experienced enough to know if you're putting on a show.
For more information about tryouts, you should read The Jeopardy! Book; though old, the information in there is still fairly accurate.