There are a few different ways to train your cat to jump through hoops, but we're going to talk about one of the easiest and most popular ways to teach your cat to go over, under or through obstacles: luring.
Luring is basically nothing more than getting your cat to chase a lure (target), such as a favorite toy or favorite treat. The target should be held just far enough away that your cat will need to follow you as you move with it; so, for example, if you want your cat to jump through a hoop, lead him first with the lure. If you want him to negotiate over or under an obstacle, lead the way with his favorite treat. Cats are smart, and he'll quickly understand what you want him to do -- the trick is to reward him for his obstacle-navigating behavior as soon as he does what you ask or you'll probably never see him jump on command again.