I always have clipped my cats claws - but as another poster said only the very tip (don't go anywhere near to the quick - the pink inner bit - if you do, it will be very painful for your cat and the claw will bleed).

My cats always let me do it while they were on my lap - I used a human nail clipper (the small one for hands) and you cut the claw tip parallel to the floor. That way the claw does not splinter.
Very quick and painless, tho I can't say my cats enjoyed it, they accepted me doing it.

However I have to some extent changed my mind over clipping - as my previous cats (living to 18) whose claws were clipped regularly - the claws thickened slightly, and eventually remained blunt for longer periods of time.

So my attitude now is to clip very seldom, only the very tip, and have lots of cat scratchers around for them to use.
My cats were confined to the garden with sadly no trees. If they had access to trees I might have not clipped at all.

While a cat is on your lap or when they are asleep, its worth while gently fingering all four paws to check that there is no claws growing into the pads or foreign bits stuck inbetwen the pads (I sometimes dislodged bits of cat litter).