Method one: First, to get just the right amount of product onto the brush and distribute it evenly, lightly sweep the polish's brush against the side of the bottle as you remove it, allowing the hairs to fan out along the lip. Next, in lieu of beginning your painting at the cuticle, just place the brush on the nail a tiny bit away from the cuticle. Give the brush a slight nudge forward and swipe it back up toward the nail bed to complete the stroke. This action takes some practice, but it should allow you to avoid your nail bed's skin altogether while accurately painting the entire nail.
Method two: Follow the same brush removal technique as above, but this time, when applying your nail polish, start around the center of the nail, polishing up to the tip. Then, carefully dab polish onto the base of the nail to blend.
And if you still get polish on the cuticles: If you're not in a hurry, allow the polish to dry completely. Then, simply rub off the superfluous polish with an emery board or soft towel. If you're rushed, wrap a small amount of cotton around the end of an orange wood stick so that it resembles a Q-tip. Apply nail polish remover to the cotton and simply "erase" the excess polish with precision.
Source: Flickr User Lidal-K.