Some people believe it's impossible to train a cat. This is not true. Cats can be trained just as easily as dogs and quite a bit more easily than children. The secret is to use methods that are appropriate to the feline temperament, which in no way resembles that of either dogs or children.
I cut my cat-training teeth on a handsome male named Sam Evening. (His sister's name was Janet, as in Sam and Janet Evening.) These kitty siblings came to me via an enterprising 8-year-old who turned his wagon into a mobile marketing unit in order to divest his family of a sudden oversupply of kittens. Capitalizing on the innate cuteness of baby cats, he convinced me to pay him one dollar for the pair, delivery included.
Shortly after the beginning of our relationship, Janet left. Perhaps I did something to offend her or maybe she just decided to relocate in a better neighborhood. I never found her. Sam, however, was with me for years.
Actually, to say that Sam was "with me" invites a misunderstanding of the nature of cats. More accurately, Sam suffered my proximity in exchange for regularly extorted payments of premium cat chow.
During the years Sam and I were together, I developed numerous insights into the training of cats. I learned, for example, that it is not necessary to raise your voice when training a cat. Volume has even less effect on a cat than it has on your children. Neither does cat training require any investment in pet yummies to be used as rewards. Unlike dogs and children, cats clearly are above bribery.
Like many endeavors in life, success in cat training is mostly a matter of timing. For instance, if you command your cat to come when he is heading in the opposite direction, you're doomed to failure. Instead, wait until the cat is walking toward you; then call him.
If you would like your cat to stay, wait until he is sound asleep. Then, softly, so as not to disturb him, give him the command. It worked every time with Sam. Likewise, give your cat the command to go out only after he has scratched on the door.
It's really very simple once you get the hang of it.
Give your cat the command to eat just as you set down his food, and he'll always obey you. Once the two of you have mastered that, give him the command to come and the command to eat simultaneously. Unless you're trying to feed him really cheap cat food, you should be successful.
For the most part, cats are above learning tricks of any sort. Some cats can be taught to sing, but I don't recommend it unless you're trying to get out of your lease.
Likewise, I don't advise teaching cats to dance. They always want to lead.