Cats are digitigrade -- they walk on their toes -- and have five retractable claws on each of their front feet and four on the back. As such, the back claws are generally worn from walking and do not require clipping. The front claws stay razor sharp, as they are when retracted when your cat walks. Clipping is necessary because nails can curl into your cat's footpad, causing infections or painful abscesses. Trim nails regularly to keep your cat comfortable and to prevent damage to your furniture caused by scratching.
To clip a cat's nails, use a stainless steel scissor-like nail cutter, and try to trim the nails before you give the cat a bath. Get your kitten used to nail trimming at an early age, so you won't have problems trimming its nails as an adult. To trim an adult cat's nails, start with two or three, and see how your cat fares. If your cat decides it's had enough, stop there and resume nail trimming at a later time.