As a person who made it through the tryouts (but haven't yet gotten the Jeopardy! phone call), this is how the contestant search works as of November, 2001.
A few weeks before the tryouts
The local TV station that shows Jeopardy! advertises the contestant search, which is held at a local shopping mall.
Show up at the mall and wait in a line. You are given a color-coded wristband. This gives you a coarse ordering for a second line (e.g, green before orange, orange before yellow, etc.) Once you get through this line (probably a couple of hours) you sit at a table with other prospective contestants. You are given a sheet of paper with 10 fill-in-the-blank questions on it. The sheets are color-coded, and there are lots of different colors, so no copying is possible. The questions are $1600 and $2000 level of difficulty. There is no official time limit, though you are using a space at the table that others are waiting for, so be reasonable. The crew does not tell you the passing score, but the consensus among those of us who passed was 7. In my contestant search, 1500 people showed at the mall. Of those, 130 passed. If you pass, you are requested to go to another location (ours was a local hotel) the next day. They tell you to wear what you would wear on the show. You should also think about amusing personal anecdotes that they could use in the interview segment of the show.
Tryout Day Two:
Show up at the hotel and mill about with the other prospective contestants. You are not in competition against each other, so everyone roots for everyone else. You are then led into a conference room, where a computer projector, some cameras, and some hardware that works with the signaling devices are set up, along with a lot of chairs, where everyone sits. The Contestant Coordinators come in: their job is to get everyone to relax. After a bit of introduction they play a message from Alex on the projector. He describes the test. You are given 50 questions in 50 different categories of $1600 to $2000 level of difficulty. For each question, the question number, category and question are shown on the projector. Then, the question number, category and question are read aloud. There is a pause of 15 seconds for you to write the answer on your answer sheet (you do not have to answer in the form of a question), and then they continue on to the next question. The qualifying score is 35 correct. The test only takes about 20 minutes.
After you take the test, some of the crew leave to grade the tests. The rest stay and help you fill out the contestant information form, which includes those interesting personal anecdotes. Then, the crew returns, and the names of the people who have qualified are read aloud. The rest are thanked and sent home. ("You don't even get a lousy copy of our home game!"). You have to wait 6 months to try again. Out of the 130 who made it this far, 37 qualified for the show. The crew claimed that 37/1500 was actually a high success ratio. Unfortunately, they always have more qualifiers than slots on the show. Only about 1/3 of the qualifiers actually get on the show. Qualification is good for a year. If you aren't called within a year, you must requalify.
Now comes the fun part. You have qualified, and now you get to play a little mock game. You stand in groups of three with the actual signaling buttons they use on the show. They tell you how the buttons work: You cannot answer until a little light comes on around the screen. If you signal too early, you are locked out for 1/2 second. Then after playing the game a bit, they do a little interview with you. After all the qualifiers do the game and interview, the session ends, and you go home and wait for the Jeopardy! phone call, when they call you and let you know when to be in L.A. for a taping. Which is what I am still doing.
Update:
Nope. Never got called. And I could have used the money since I was unemployed at the time. <SIGH>. I'll just have to try again the next time they come through.
But I'm not getting any younger.