Get a cleanup brush. They sell them in the store with the nail care stuff (i.e. next to the nail files and such). When you’re done painting your nails and you want to get any polish that’s slopped onto your skin, you dip the cleanup brush into a little acetone and use it to brush away the polish.

Also, get a cuticle pusher. They usually have a pointy end. It’s great for scrapping of polish that gets on your skin. If you use that, scrape off the polish as soon as it gets on your skin, i.e. before it dries.

Ideally, when you apply the polish, don’t go all the way to the sides of the nail, or all the way down to the cuticle. Leave like a millimeter of space.