Contrary to popular belief, it really is possible to train your cat. As with all training, it should be kind and based on positive reinforcement, rewarding correct and ignoring unwanted behavior. Cats learn through association. In practice, this means that a behavior (an action) followed by a positive consequence (a reward) will be repeated. On the other hand, a behavior followed by a negative consequence, or simply ignored, tends not to be repeated. As you think about training, think about what you want the cat to do, why she should want to do it (what is her motivation?), and when you want to give the reward. Figure out what motivates your cat. Most dogs are motivated by either toys or food, which makes dog training considerably easier. Cats tend to be solely motivated by food, but, unfortunately, this only works when they're hungry!
Teaching your cat good manners is important, and the training doesn't have to be a chore. Cats are highly intelligent animals and can be trained to good behavior no matter what their age. As with all training, kindness and positive reinforcement are important. Be patient, reward good behavior and ignore unwanted behavior, and soon your cat will be well behaved.
Training is ongoing. Your cat may already be well behaved when she joins your family, even so, her training should be ongoing. Your cat can pick up a bad habit quickly and it may take a while to rid her of the habit, especially if she has been allowed to get away with it for a while. However, bad behavior can be stopped by using positive reinforcement in her training. When you train your cat in this way, you encourage her to display good behavior, and ignore her when she displays bad behavior. For example, if she jumps on the kitchen counter you should respond by lifting her off and then ignoring her. If she stays on the floor, she should be praised and rewarded. Your cat will soon associate the praise and reward with the correct action, and stop the behavior that gets her no attention.
What do you want to teach your cat? As you plan your cat's training, think about what behavior you want from your cat, why she should want to do it and when you will reward her. If you can find a treat that your cat is particularly fond of, it can act as a motivator for your cat and will aid you with your training. Training a cat is very different from training a dog. For example, you won't be asking your cat to perform a range of actions such as "sit" or "heel." However, you can teach your cat to respect certain parts of your house, and train her so that she knows she is not allowed to scratch the furniture. Provide her with a scratching post and each time she uses it praise and reward her. If she does scratch the furniture, gently move her away from the furniture and then ignore her.
Cats are naturally clean animals and will usually seek out a litter box. If your cat doesn't use her litter box check that it hasn't been moved, that it is placed in a quiet area away from her feeding area and that it is readily accessible and clean. If your cat is upset, she may seek out places other than her litter box to relieve herself, but she can be coaxed back quite quickly by changing the cat litter you use or by re-establishing her litter box area.
If you really want to take training to the next level, you can actually get your cat to walk on a leash. You'll need a collar, harness, leash, and lots of patience. Kittens are generally easier to leash train, but with praise and kindness, many adult cats can be leash trained as well. Over several days, get your cat used to wearing the collar and harness for several minutes at a time. Let him prowl around the house with the leash on, and eventually he will be confident and trusting enough to go outside for a short expedition in a quiet, safe area. Make sure you offer him treats and encouragement, and don't push him too fast or your trips outside will be frightening, instead of fun.
Cats catch on very quickly and are easy to train. A well-behaved cat is a credit to her owner, so encourage good manners through praise and reward, and soon your cat will understand what behavior is expected from her.