It is recommended you get a cat used to having it's feet handled from an early age. This can be done by gently massaging your cat's feet. Some of my cats are less than thrilled at having their claws trimmed.
In such a case I recommend you only trim a couple of claws per session, or do as I sometimes do and gently trim then when the cat is napping. If you have a particularly reluctant cat, there is a product called Felifriend you could try. This is a synthetic pheromone you spray on your hands, it may assist in calming your cat down.
Hold the cat's paw in your hand with your fingers on the underside and your thumb on the top.
Gently apply a forward pressure to one toe. This causes the claw to come out of the sheath, which makes it more visible.
Cat Claw 1
Notice how in the middle of the claw is pink, this is the quick and it contains blood and nerves. This must NOT be cut as it will cause pain and bleeding. If you do accidentally cut this, apply a styptic pencil Silver Nitrate sticks or Potassium of Permaganate to the claw to stop the bleeding. If you don't have these products, ordinary household flour will do. The claw should stop bleeding in about 5 minutes.
Cat Claw - Showing Quick
There are several kinds of nail clippers you can use. I use regular nail clippers for humans, but you can also purchase clippers specifically for cat's claws, these should be available from your vet or pet supply shop. Nail clippers should be very sharp as blunt ones will crush the nail, not cut it.
Clipping cat's claw
Aim to trim between the tip of the claw and the quick.
Cat's claw trimmed
Some people trim their cat's back claws, I don't, this is because my cat's tend to wear their back claws down naturally. I trim their front claws approximately every 3-4 weeks.