To the OP: I've never done barrels, and the closest experience I have is just running around random objects for the fun of it. If you wanna get into it then set up a pattern and walk it, make sure your horse is conditioned (its hard on the joints!) and fed for what you are demanding they do.
It also helps to have a horse that loves it as much as you do. I'd suggest trying to find someone who can help you and give you some pointers if you are looking into seriously getting into the whole competitions and past local shows and also get a new horse for it as well if possible.
But for now, do your research! There is lots of helpful advice in books, youtube videos (look for accomplished racers and watch them, study them and see if you can't pick up the little things they do that make them work.), and slowly put it into practice.
Just please be considerate of the horse, and keep in mind the risks. I don't know them all, but I know arthritis and other problems arise from years of barrel racing oftentimes, so you are going to want to make sure you can afford to take care of your buddy if he does hurt himself working for you.