I have always clipped them on my own. I'm really lucky with Nakita, she actually purrs when I cut them. I think when you start training a cat early on (by handling their paws, massaging them etc) they will be more easily accepting of the clippers.

I also clipped the nails of the cat I had with my family. This was harder since this Siamese didn't want them cut. It took two people to cut them - I would hold her while my mother would cut the nails.

Actually, I've never known anyone who took their cat to the vet to clip the nails till I came on the internet and read stories like yours.