Never use your nails as tools.
Never “pick” your cuticles. This can lead to infection, then damage or even loss of the nail.
Keep cuticles soft and supple. The skin splitting around the cuticle area and the side wall is a sign of dryness, prevent dryness with cuticle oil.
Keep your cuticles pushed back. For the same reasons as in 3. The tighter the skin around the nail is, the more chance it will dry and split.
Make sure you clean out from under your nails everyday. Debris and bacteria harbor themselves in this area and can cause infections.
Keep your cuticles pushed back.