I'd clip them myself when they started getting caught on things, about once a month or so. She hated it, so I'd only do one paw a day (taking perhaps 30 seconds), and continue the next few days until all the long nails were done. And I would always follow up immediately with something yummy. Tuna omlette was her favourite, as well as mine, since I'd eat most of it first and give her about a quarter. Everyone wins!
You can get it done at a vet, but unless you have to go there anyway, it's a bit of a waste to put the poor cat in a carrier and car and all of the associated distress just for something that only takes three minutes (unless your cat loves going to the vet for some reason and isn't upset by all of the associated things to get there). I asked the vet when we first got our cat, and she said that it's nicer to do it at home if you know what you're doing, and showed me how. Just keep your clippers clean and sharp, and don't clip the black line running down nail and you're good.