If I recall correctly, nails (finger nails or toe nails) grow by adding matter at its base. So for instance, if you would draw a dot at the very bottom of your nail, it would end at the top in a couple of weeks.
I was wondering how this works with hair. Is new hair added at the bottom and the old hair 'pushed' away? Or does hair consist of layers that always try to get further and further (that would mean longer hair is thicker than shorter hair). And is this wayof growth similar to how grass grows?