Remember, start handling your kitty's feet at a very young age, if you can! This is a vital step in getting him used to the feel of hands playing with his tickly feet.
If your cat is older and doesn't want you handling his feet, try wrapping him in a towel and cover his head. This may aid some cats in remaining calm during the clipping process. Be gentle and never force your cat if he is violently opposed to having his feet handled. No blood need be shed. Alternatively, buy yourself a beautiful cat tree that matches your decor.
If you can, start clipping nails when your cat is very young. Here we have a three-week old kitten. Claws are already very sharp. Though you might not have the opportunity to start your cat this young, begin when he or she is as young as possible, or when you first acquire your cat. Start by handling your kitty's paws gently several times a day. This gets them accustomed to hands on their paws.
Even at a very young age, kittens have super sharp needle-like claws. If you handle a tiny kitten, they will cling to you like velcro, and it can hurt (or at the very least, snag your clothing).
When a cat is resting, his claws will be retracted. You probably won't see his claws. Start clipping nails as your kitty sleeps and is completely relaxed.
You can use cat claw clippers, but it is not necessary. I use human nail clippers or small nippers, as shown in the photo. When actually clipping your cat's nails, be careful not to clip the quick (the vein that runs inside the nail). Just clip the very tip of the nail.
If you keep your cat's nails trimmed regularly (such as each week), the nails will develop a rounded appearance. Your cat will still go through the motion of scratching, but will cause no damage (and will save your skin if he or she likes to play rough).