Although cats aren’t exactly trainable in the way dogs are, it is possible to modify their behavior. The trick is that you have to make them think that the change was their idea the whole time. So you need to think like a cat. For example, in the feline world, food is a big motivator. If you leave food on the counters, your cat will go up there to forage, whether or not this behavior is "allowed" at your house. To counteract this counter surfing, you need a deterrent. When you are around, you can use a water-filled squirt bottle and commando tactics to remind kitty that the counters are off-limits. The most effective corrections are ones that don’t involve you, however. For example, some people set up booby traps such as upside-down mousetraps underneath a piece of tinfoil. When kitty leaps up on the counter, she springs the trap, which makes a lot of noise and causes her to jump down to get away from the evil counter demon. A similar approach can be used for cats that molest garbage cans.
Cats are very territorial and have a sense of smell that is far superior to ours. They don’t scratch furniture out of spite. They do it to mark territory. As most people can attest, when you yell at a cat for scratching the furniture, kitty generally just looks at you like you’re an idiot and proceeds to wait until you aren’t around to engage in her destruction. A more effective approach is to keep your cat’s nails trimmed and buy or make her an appealing scratching post that she can really sink her claws into. Rub the post with catnip, so she feels it’s a feline-friendly place. Then attach some double-stick tape or contact paper to favorite scratching points on the sofa to make it feline-unfriendly (cats hate sticky feet). Praise the cat for scratching the post, and if she heads for the sofa, clap your hands or make another loud noise to startle her away.
The key to changing your cat’s behavior is understanding what is motivating her actions. Once you understand what she’s doing from a feline perspective, it’s easier to find creative solutions to solve problems.