Pinkbear, Polly has had no teeth for a long time. After a while the gums harden and the cat adapts to not having teeth. Polly's weren't removed. She just yawned one day and I was amazed to see only gums!
I trim claws with the all-round style trimmers. These are harder to use as you have to get the cat claw through the hole. They are better imo, because they cut the claw from two sides, preventing splitting. However, Polly's claws are getting so thick they won't go through the hole anymore, so I'm going to buy the scissor type Sazkat refers to.
Just beware of cutting the quick, which is a pink bit running inside the claw. It doesn't run to the tip. You can usually see this in a good light.
Take a look at this useful vid:
http://uk.youtube.com/watch?v=Ut886IEvn9w