Learning cat behaviors before you start training them would be an good idea for anyone that is going to train a cat's behavior.
A cat can jump and land on its feet as this is a natural instinct for a cat. When a kitten is born the cushion in its paws are not developed with the cushion to land on its feet. It takes about 7 weeks to develop the cushion in a kittens paw for landing. A cats bone structure is unique to other animals as the bones are flexible, cats have no collar bone, which enables them to twist and bend their bones. A cat can jump a great distance without sustaining any injuries.
With this behavior, you will want to teach the cat to jump hoops, sticks, or off the scratching tree. Letting a cat jump from extreme heights will cause injury to the cat.
Cats have a unique hearing ability; they are able to hear high tones and pitches, like opening a door or a can of food. Cats also have unique smelling abilities. The reason a cat will scratch or urinate on the floor , rub its self up against a door or furniture, is the cat is leaving their scent in those areas so they will be able to come back and know they were there, in other words marking its territory. In addition, if another cat or animal comes along in the area a cat will know this. Cats can also smell with their mouths. There is a gland called Jacobson's organ, it is a sac in the cats upper mouth filled with blood, as the cat smells the scent and the slightly opens their mouth and upper lip, this allows the scent to be carried in and to the sac, which it will carry the scent goes to the cat brain. This mostly happen to male cats when a female has urinated.
Knowing these natural instincts and behaviors can give you some insight training your cat. With behavior training you will want to make sure that you allow your cat the ability in some way to play out its natural instincts and behaviors.
When training a cat for behaviors there are some things you need to take into consideration. Aggression, especially in older cats, can be caused from illness or other cats in the home. You may want to contact your vet to have your cat checked out to see if it's alright at this time to train a cat.
Depression and anxiety can play another part in trying to train your cat. If a cat is separated by a recent owner the cat can become depressed. Stress is not uncommon for a cat. If you think that your cat has depression or high anxiety, this would be a good time to take him to the vet. Vets can talk to you about some of the things that may be causing this. There are also medications that a vet can prescribe for the cat to help with depression and anxiety.
Never hit a cat for punishment, he will learn to fear you, and fearing will be a behavior you will not be able to control or retrain. When they do something that is not right, ignore the problem unless you catch them in the act, you can associate a noise with that behavior you don't like, or in a stern voice tell them NO.
If a behavior is becoming impossible, you may have to resort to the baby proof home, all containers that have food in them have a lid on it. Make sure that the counters are clean and have nothing that a cat would want to play with.
You will want to start training your cat or kitten almost immediately after you get them. This will stop many unwanted behaviors and hopefully not let any new bad behaviors to start.
Healthy cats need healthy relationships with their owners. Good Luck!