In order to tame a gravedigger to mount it you must first have completed The Gravedigger of Drefia Quest. After this you must then use the Nail Case a total of five times, once per finger, in a row successfully. It's believed that waiting a few moments between uses increases the chances of taming. You can fail at any finger. Also, note that the Nail Case will not break.
Succeeding:
# You carefully cut the nail of the gravedigger's thumb.
# You successfully manicured the forefinger of the gravedigger.
# You successfully manicured the middlefinger of the gravedigger.
# You actually manicured the ring finger of the gravedigger without a problem.
# You did it! A completely manicured gravedigger is ready to follow you as your own personal trusty mount until the bitter end!
Failing: You failed to manicure the nails of the sensitive gravedigger. Before you can make amends, the creature runs away in agony.