Training horses for professional racing is somewhat similar to training horses for other forms of entertainment. A career as a horse trainer is time-consuming and can be somewhat dangerous. Even the best trainers have been bitten and kicked. You really have to know how to handle horses.
Horse trainers start out low on the totem pole, taking care of the horses, grooming them, and exercising and saddling them. Riding comes later, or can be done off-hours. Having in-depth knowledge of equine health and psychology is essential for this job.
If working at a race track is what you really want to do, you should start by hanging out near the stables and introducing yourself to the trainers. Ask if you can volunteer. That might mean cleaning out stalls. Show that you really want to be there and are willing to do all jobs to advance in this profession.
Once you are interning, volunteering, or working with a professional trainer, you will want to apply for a license through your state's racing commission. When taking the exam, you will be tested on racing rules and regulations and horse knowledge. For more information, contact the American Quarter Horse Association.