Qualifications
Barring some magic Disney-type moment—where some horse owner plucks you off the street, taps you to be a jockey, and you and a horse become an underdog team that nobody ever expected to make the pros—you'll need to go to a jockey training academy.
Horse racing is a small community. You're going to need the training and certification from a verified jockey school, and you'll also need their job placement connections to get paired with a horse owner and your first gig. After that, you'll need an agent to make sure you're not getting taken advantage of and that you're given the best opportunities possible.
The jockey school in the U.S. is partnered with Kentucky Community Tech College. You're required to have graduated high school or have earned a GED, and you'll be enrolled in a program in equine studies (source).
The biggest qualification for the job, other than being able to ride a thoroughbred, is being just the right size. Do we need to say it again? If you're six feet tall, this dream of yours just isn't going to happen.