I clip my cat's claws myself. I was a bit scared at first, as she is my first cat, but now we have both got used to it, it goes pretty well.
Here are a couple of things which may help:

TIP 1: If your cat is still quite young, then wait until she is lying on your lap and you are both relaxed, then gently "massage" her paws so her claws "slip out". I knew I wouldn't have time to get Ally to the vet for clipping, so when she was still small I started doing this - so now she associates the feeling with a cuddly / relaxing time in front of the TV. and not only with clipping.....

TIP 2: I tried the proper claw clippers, but I found them difficult to manage. I use a pair of normal (human)nail clippers, and only take off the very tip, so they don't split or anything.