I used to have a dog that would chew his own nails so that we wouldn’t have to cut them!  He hated having his nails cut!  Sometimes, though, we had to help him keep up with the job.  We can all benefit from knowing how to properly cut our pet’s nails.  We have added a video to our website that shows how to trim a dog’s nails and it can also be found on YouTube.  YouTube video  A cat’s nail trimming is essentially the same.  It is actually easier, if you can get your kitty to hold still and cooperate!  But that’s another story. 
Keep in mind that as you get near the “quick” (the blood vessel) the nerve sensitivity increases and there is a pinching sensation that some pets anticipate will be worse than it actually is.  Be sure to go slow and try not to cut the nails back too far.  This will help your pet build trust in your ability and minimize fear of the procedure.