You need to cut their claws regularly. This is very important for an indoor cat, as otherwise they can end up damaging furniture, carpets, humans, other cats, etc.
I use human nail clippers to cut my 2 cats' (front) claws and have had no problems.
I've tried before, he won't let me.
Last time the vets did it, they can restrain him better than I can, and he's due there next month so will get them to do it.