scissors, knives, scrapers, biting, tearing, specialty tools and even simple natural wear are some of the answers.

For more details and some interesting lore check out the FAQ on Trimming Nails

Also covered in How did people cut their nails before the nail clipper was invented? Did they bite them? If so why is it now considered a bad habit?

Not to discourage other answers though. Personally I feel like this question has received some good answers but hasn't received a great comprehensive well sourced answer yet. Maybe the question is just too large and covers too many peoples for one historian to be aware of all facets.