If your horse tries to buck, drive it forward with your legs and keep its head up. By keeping the animal level, you’ll make it impossible for it to let out a big buck. You may even need to hit the horse with your riding crop, just behind your calf, to drive it forward. The punishment should not be abusive, but it should be uncomfortable enough that the horse learns not to buck again.
If it attempts to rear, also use your legs to drive it forward. Be sure to lean forward as the horse’s front feet leave the ground so that your upper-body weight can help to push the forehand downward. (If a horse rears and the rider leans back, he can cause the horse to fall backward.) Once again, the stick is the correct punishment. The horse should be made to gallop as part of the correction for his unwillingness to go forward, as demonstrated through rearing.
Before a show, give your horse a fairly hard workout, so that it’s a little tired. If the animal still looks as though it’s fresh at the show, longe it before you get on. If the horse is a little tired, it won’t be so prone to buck or rear.