When you hold the rabbit's nails up to light you will see the "quick," which looks like a pink nerve running through. As long as there is sufficient dead nail beyond the quick, it is okay to cut the dead portion.
I don't know how often you are supposed to cut a rabbit's nails. I cut my rabbit's nails once every 2 months, but they run around the apartment so much that by the time I get to them they have already lost a few nails by snagging them on the carpet!