I train my cats. Not to use the litter box. If they don't know that when they arrive in this house, there is no hope. But since I am a frustrated dog owner I train the cats to do tricks. Just simple ones like sit and shake. A smart cat can speak and help himself to a treat. I use behavior shaping and persistence and rewards to achieve the desired results. Similar to training a dog, only with less trust and love, and more over and over and over again. I could teach you how to train your cat to sit and shake because most cats in my experience can do those tricks, but I won't bore you. There is not a big market for trick cats.
The training I am most proud of is handling behavior issues. Our cats live with us, they sleep with us, they sit on my husband's lap and are fed very expensive food continually. But sometimes an undesirable behavior crops up. Then what do you do? Get rid of the cat? That is harder to do than you think on a number of levels.
This is what I do. Look at the behavior. What is the cause? Sometimes researching the cause requires a trip to the vet to rule out illness. But often it is that the cat wants to shape my behavior to do something more or sooner. Those behaviors are the easiest for me to change.
For example, Rudy, who lives to eat. He would wake us from sleeping in order to be fed. We have an automatic feeder that feeds him in the night. He waits in the basement for it and joins us in the middle of the night after he has eaten.
Dodger is old and thin and needs to eat more often so we started feeding him wet food in the morning. This has led to a behavior issue of being awakened by a cat who decides that it is time to eat, even if that time is 4:30 in the wee small hours. We shut him out of the bedroom but he bangs on the door. Squirting with water would be my first solution, but our cats like to be sprayed with water. But not perfume. I have so natural honeysuckle spray. I open the door and spray. The cat runs and misses the spray for the most part but also avoids the door because he hates the smell of the perfume. Problem solved.
If only all the problems in my life were so easily solved. By natural honeysuckle spray.