The claws of a cat keep growing, which means you need to provide your cat with a scratching post to help it remove the dead nail and sharpen up the new one. Since cat’s claws can be sharp and deadly, you also might want to trim them occasionally.
The trick is doing it safely without those same claws shredding your flesh like you stuck your arm into a spinning lawnmower blade. First, calm your cat. Second, don’t yell or punish the cat if it squirms. Third, be prepared to bleed profusely so get a First Aid kit handy. Then try practicing clipping one or two nails at a time.
The trick is to get your cat comfortable with the entire nail trimming process so reward it afterwards. The other trick is to avoid losing more than a pint of blood in the process as well.