You can use various nail clippers for this job. There are the regular human nail clippers, pet nail clippers, and the clippers that hold the claw in place. You can use any of these for this purpose.
Trimming Cats ClawsTry to begin with the nail clipping when your cat is relaxed. If the cat is nervous or stressed, it will be more difficult for both of you. It's easiest if you start trimming claws when your cat is a kitten, so they will get used to it. You can hold your cat in various positions. You can hold them in your lap or put them on a table. You can also hold them in a cradle-like pose. One of my cats is a very frisky fellow but he loves being cradled, so this position puts him in a mellow mood. If your cat is really agitated, you can wrap them in a towel to prevent yourself from being scratched.
While holding the cat, use your other hand to gently take their front paw. Softly squeeze the paw you are holding. The cats claws will be visible, they are clear. Use your clippers to trim the tip of the claw. Don't go to far up to the "quick". This is where the blood vessels are. If you cut it, the claw will bleed. If that happens, use cornstarch to stop the bleeding. You only need to clip the very tip of the claw.
After you have clipped the claws on the first paw, proceed to the other front paw. If your cat is too stressed, take a break. You can always continue in a couple hours or a day later. Rear claws don't grow as fast and don't need to be trimmed as often. You should still trim them occasionally.
After the clipping is complete, pet and stroke your kitty to relax them and offer a small treat as a reward. Once you do this a few times, both you and your cat will adjust. It's not difficult to trim your cats claws at home.