We want to know how you got on there in the first place. I can't wait to watch your return episode, hopefully someone can post it here
If you sign up at jeopardy.com, they will notify you when they next schedule an online test. The online test displays questions every 15 seconds - you type in your response. It doesn't have to be in the form of a question. About 70,000 people take the online test every year.
There is a cutoff score for the online test. They won't say exactly what it is, but there's widespread speculation that it's 35/50. If your score is above that, you may be randomly selected to audition in person. They travel to various cities to run auditions - mine was in Washington DC. About 3,000 people are invited to audition.
At the audition, you take another, in-person test - presumably, in case you had someone else take the online test for you. You also play a short mock game against your fellow auditioners, using a real buzzer, and you have a short "personality interview." There's a written application too, which has things like "five interesting facts that Alex could ask you about on the show." Then you go home. You may or may not be added to the contestant pool - no one will tell you whether you've made it into the pool. You just wait by the phone for the next 18 months, and then if you weren't selected you can start over again with the online test.
About 400 people per year get "the call" and are invited to be on the show. Almost exactly 7 months passed between my audition and the call, but I talked to some people who were called almost immediately and others who waited more than a year.
The whole process was actually really fun. Just auditioning was a great experience.