Some people say that cats cannot be trained. It is true that it is difficult to train a cat in the way you would a dog, to sit and stay, for example. But cats can be trained to do basic activities in the correct way, for example using a litter tray. They can also be taught not to chew and eat unsuitable items. And some cats can also be trained to do a few things which are unusual for a cat, like walk on a lead. Here are some FAQS concerning cat training
Unlike dogs, cats are not anxious to please their owners. They will not do what you want just because you praise them for doing it. So you have to find something the cat wants. For most cats, food rewards work well, particularly tasty cat treats. Positive reinforcement works better than negative, ie a cat is more likely to do something because he gets something nice if he does, than to stop doing something because a nasty event happens. This means that yelling at a cat to stop doing something rarely works. And never, ever smack a cat for doing something bad; you are likely to simply confuse him.
Most cats are taught to use litter trays by their mothers, when they are kittens. But sometimes for some reason this does not happen. And occasionally you may have to train an adult cat to use a litter tray.
Place the litter tray in a quiet place, away from general traffic through the house, and well away from the cat's food. Make sure there is enough litter in the tray for the cat to scratch. At intervals, and particularly if you catch the cat scratching elsewhere or looking like it wants to 'go', gently put the cat in the litter tray. Praise it and offer treats if it urinates in the tray. It should soon get the idea. Never shout at the cat for soiling elsewhere, and don't rub its nose in the mess; it will be frightened and confused, and not understand what you mean.
This should work, but if there are problems, try putting the litter tray somewhere else, or using a different type of litter. If you have a large cat, make sure you have a large enough litter tray. And make sure the tray is kept clean, as cats hate dirty litter trays.
Sometimes even well trained cats take it into their heads to urinate in the wrong place, and a bathtub is a favourite for this. It is always harder to stop a cat doing something bad than to persuade it to do something good, as positive reinforcement such as treats cannot be used. Firstly, try to find out why the cat is doing this. It could be because of a smell creeping up through the pipes, that the cat associates with its litter tray, so it perceives the bath as an alternative litter tray. It could be that the bath, or something in the bathroom, has been cleaned with a product containing ammonia. Ammonia smells similar to cat urine, so again, the cat may think this is an alternative place to 'go'. It could also be that the cat does not like the location of its litter tray, or finds it too small.
If you can't find out what the problem is, and are unable to stop the cat using the bath, one simple way of solving this problem is to keep the bathroom door closed. Or you could keep a little water in the bath at all times. Doing either of these for a short time may solve the issue. If not, try keeping the litter tray in the bathroom; it may simply be that when it wants to do its business, the cat prefers a nice quiet bathroom to anywhere else in the house.
No-one knows why, but some cats develop a taste for houseplants, or want to chew on items such as electrical cords. In these cases, again you cannot use positive reinforcement. If possible, keep houseplants and electrical cords out of reach of cats. You could also try painting or spraying the items with something harmless, but which does not taste good to cats, such as lemon juice. Another way is to squirt the cat with water every time it tries to chew an unsuitable item. It won't associate the spraying with you, but will hopefully learn that nasty things happen when you try to chew plants or cords.
Every cat has to use a cat carrier at some point, as this is the only safe way to take a cat to the vet or a cattery. But cats quickly come to associate carriers with vet visits, and will often refuse to get in one. The bes way to accustom the cat to getting in its carrier is to leave it open in the house for at least a couple of days before the vet visit. Put a favourite blanket in the carrier, and try to get the cat to use it as part of its normal living space. This should make things easier on vet days, but if the cat still struggles, wrap it gently but firmly in a towel and then place it in the carrier. If your cat is especially difficult, you might want to get a top-opening carrier, which is much easier to use.
Not all cats can be trained to walk on a lead, but many can. Get a harness with a lead that attaches at the cat's back, not its neck, and ensure it is one designed for cats, not dogs. Leave the harness out for a few days so your cat can get used to the sight of it. Next, drape the harness over the cat, without fully attaching it, when giving the cat a treat. You'll eventually be able to move to securing the harness around the cat. Once your cat is comfortable with the harness, attach the lead to it, and let your cat wander freely around inside with it. After a few days, start holding the lead sometimes. Then finally, go outside with the cat. Just try it for a short time at first, and somewhere quiet. Eventually your cat may be happy to go for walks with you, using it's lead.
Hopefully these examples will have given you an idea of how cat training works, and you will be able to adapt them to other situations. Good luck!