Next: More Expert Cat Advice
Cats have different behaviors than dogs that must be dealt with. For example, we try to teach our cats not to scratch the furniture, while we try to teach our dogs not to chew the furniture.
Some things are infinitely easier with a cat. Show a cat the litter box once, and potty training is usually a done deal. With a puppy, potty training generally takes weeks. But in general, training a cat must be done repeatedly, patiently and at the cat's own pace. A dog is much more adaptable to the human's schedule and to intensive training.
In the case of both cats and dogs, I recommend positive reinforcement as the motivator. Punishment can have a serious traumatic effect on a cat, while dogs can accept some punishment, as they are pack animals and used to a complex social structure. But repetition and positive reinforcement are the two things that are going to earn you the behavior, as well as the respectful, affectionate relationship with your animal that you want.