Your cuticle is there for a reason; it's the skin barrier that prevents bacteria from entering your body. Cuticles should not be cut off! On the other hand, you can't let them grow haywire either, because overgrown cuticles can suffocate nail growth. The solution: Apply a cuticle remover (not a cuticle cream or oil) to the nail. Then, using tiny circular movements, take an orangewood stick and gently push back anywhere the cuticle skin touches the nail plate. Hold the stick at an angle to ensure that you do this gradually and gently, without going above the cuticle. The white stuff left over by the cuticle, the ghost of the cuticle, is called pterygium, and this should be cleaned from the nail as well.
Anything left hanging after you have pushed back your cuticles is okay to cut. Using a cuticle nipper, remove the remaining hangnails. Here is the one implement where you may want to spend a little money to ensure that it is sharp. A dull, cheap cuticle nipper will not allow you to get at the hangnails and may create nail damage.
Moisturize, Moisturize, Moisturize
Moisturizing your nails every day is important to maintaining healthy cuticles. Every once in awhile, give yourself a treat and massage an oil, or your favorite moisturizing cream, into your nails, up your fingers and hands, past your wrists and up to your elbows. Jojoba oil is excellent for skin.