I guess some people aren't good painters and so they usually paint everywhere on their nails and even on their skin. And sometimes the polish on the skin are really difficult to get rid. So i have a few solutions for you.
1. Practice makes perfect. Keep painting and training and you can do better.
2. After your nails have dried from painting, use a cotton bud dipped in nail polish remover and gently rub off the excess.
3. Use tape to paint (troublesome).
4. When painting, use a cuticle stick to get rid of the excess before the polishes dries.
5. Paint your nails at night, at least an hour before bed time. And when you shower the next morning, the skin around your nails will soften and excess polish would be easy to get rid with a soft towel. Alternatively, you can soak your hands in warm water and just rub the excess nail polishes around your cuticle off.
Thanks for reading folks!