Your age would be a big deciding factor in a lot of things here, but regardless, I say talk to him about common interests (assuming you are riding horses?) then horses might be a great topic.
Be yourself, if your conversation seems to be going well then see if he wants to "get together" for a drink or lunch or something. Try the "hey, I'm kind of hungry. Feel like grabbing a bite to eat?" line, then head down to Mc D's, keep it light at first. Things will or won't happen in their own time. (this also depends on your age too, and if you would need a chaperon... which could get kind of weird. If you are supposed to have a chaperon, just try to hang back a little chat a little longer.)