Help i sliced part of my thumb off!

Patient: I was messing around with our new miracle vegitible slicer today and whilst slicing an apple i accidently sliced a medium slice of my thumb tip off. Its about oh maybe half a centimeter long and 1 or 2mm deep, not to deep but still. Oh boy did it hurt and bleed.There was no bone showing and no veins were cut into. I was just wondering will it grow back? How long is it gonna take and what should i do to take care of it? Any help is appreciated thanks.