I have never wanted to be on TV but difficult child has tried out and been called back 3 times, once as a child and twice as a teen. I am pretty sure it works the same way for adults and kids. You come to the location, twice it was in my city, and once we took a 3 hour train ride, at a set time. The children's version was random selection so the first thing they did was give a 50 question test. They loved difficult child's personality but he didn't pass the test (lots of sports and pop music, not two of his top areas). The teen tryouts didn't involve a test there because these kids had already passed the online test. They were interviewed and played a mock round of the game. Parents weren't allowed in. difficult child had a great time but wasn't selected. Basically, they said they were looking for (for the teen tournament), kids who were diverse even more than bright, because every applicant was bright. As a white male, difficult child was in an over-represented group, based on what I saw. I have no idea why they choose who they choose. difficult child plans to try again as an adult; he doesn't want to bother with college Jeopardy because it has a limited payout.
My suggestion to you is go for it. Not many people can say they passed the Jeopardy test and got called in... You must be very bright.