This sounds like the Chevy commercial, right? Walter, the cat who jumps into the water and fetches a stick, and herds cattle?
Walter is probably a stunt cat, who's undergone years of training and costs thousands per day to rent for your commercial, and comes with a cat wrangler. Mine is just an ordinary pet cat, who happens to love those little cat treats. And I have no professional training at all in this, which means you can do it, too.
Motivation and Caring
That bit about the treats is the key, and I think any animal trainer would tell you that: you have to have some motivation for the animal. For some service dogs, especially military or police, it's the chance to play with a tug toy. Food is pretty common, though. Try food. If that doesn't work, you might be out of luck, but you know your cat better than I do. Maybe there's some toy he really enjoys? I'll assume "food" in the rest of this, because that's pretty universal among animals.
You are not going to be abusing your cat. Don't think of this as making Kitty do something he doesn't want to do. If Kitty doesn't feel like it today, then drop it. Come back later. If he never wants to, then forget about it. You love your cat.
At zoos, they train the animals to lift their feet, turn around, lie down, or otherwise do things the veterinarians need them to do. It's better than sedating them. Watch this video from the Oregon Zoo:
What to Aim For
Pick a task your cat might normally choose to do. Jumping is such a task. Swatting with a paw is, too. Swimming is not. Don't try to teach your cat to swim out and fetch a stick like Walter in the Chevy commercial, unless you're very, very good at this.
Jumping through a reasonably large hoop is a task your cat probably doesn't mind. Jumping through a very tiny one will make him anxious. A hula hoop would be fine, but it's more impressive if the hoop is a little smaller, like mine.
What Not To
A cat is not a dog. This might seem obvious, but you can't expect Kitty to be as eager to please you as your dog might be.
On the other hand, no one's impressed if your dog can sit and offer a paw. But they might be to see your cat do it.
Start with an Easy Task
For the hoop trick, put the hoop on the floor. Hold the treat behind it. Kitty will probably try to walk around the hoop. You saw mine do that in the video. Don't allow him to. Move the hoop so he has to walk through it. Keep doing this, then wait a day and do it again. Don't be surprised if the cat forgets everything you taught him and tries to walk around the hoop again. You're more persistent than he is. And you'll never get annoyed with Kitty, will you?
Keep the training sessions short, 15 minutes or so. If the cat is losing focus or wanting to be elsewhere, just stop.
Watch this video from the Texas Zoo. The trainer is patient and encouraging.
If this mighty king of the jungle who could kill you without even breathing hard can do it, do you really think your cat is untrainable?