I didn't buy my guy straight off the track but the man who sold him to me didn't do much with him so he still had the same mental state as one fresh off the racetrack.
I started him with tons of roundpen work before I even got on him. Making him learn my verbal cues for walk, trot, canter, whoa and easy. I did have a trainer to help me out a few times a month (still do) so I do recommend one if you haven't brought one along before. Start slow and PATIENCE!!!! teaching verbal commands has saved my butt too many times to count.
When starting under saddle be relaxed and do lots of circles, transitions, change of direction etc. They tend to get bored and wound up if they don't have anything to keep their minds occupied. My boy loves it when I talk to him while riding it seems to soothe him and he listens a lot more to my voice than anything else.
Hope this helps!