How to take care of your nails?
Clean your hands (and wrists) with soap and warm water. This will prevent the build up of bacteria on your hands and may prevent dirt under your nails getting worse.
Use a clean nail brush to clean under your nails. Make sure it is clean, because otherwise you may be transferring dirt and skin cells back under your nails (yuck!).
Wash off all the soap and dry your hands on a clean, soft towel.
While your nails are soft, trim them. The more often you trim them (before they get too long), the stronger they will grow out to be.
Use a nail file (only use in one direction).
Use a hand lotion/cream. Don't worry if you can't though, because your body will usually provide natural moisture for your hands.
Use cuticle oil. It strengthens your nails and helps you push back those cuticles!
Do this routine every day. (But only cut your nails when necessary, otherwise your nails will be too short). Also remember to be careful with your hands.