I auditioned for the teen tournament when I was 15 or so. You had to call in to get an audition spot, then we drove 8 hours up to St. Louis for the actual auditions. I passed the paper-and-pencil test (which I assume has been replaced by the online test), but froze up in the next step, which is much more like being on the game show. (They ask you some interview questions, then you have to ring in and answer against 2 other auditioners.) It was fun - I had a good time doing it, even with the drive and with not being picked.

La Texican, you'd have to cover your own travel expenses to get to the filming, but there's no entry fee or anything like that.