If you run track, you must have strong legs. That's good in horseback riding, because you use them to hold on. No, you don't need your own horse. Find a place near you that advertises lessons. There may be English lessons or Western lessons available. I'd try both to see which you prefer. Of course, if you live in cowboy land, maybe you want to ride the way most of your buddies ride. On the other hand, many places have mostly English. Both are cool in their own ways.
Horses are great, but they're big, so be careful. Be honest with the teacher...if you're a beginner, say so. Don't be embarrassed...everybody starts sometime. If you have trouble finding a stable, check out 4-H in your area...they might be able to hook you up. Good luck!