I learned the hard way to put a mat down under my computer chair - I've had a couple from Staples I wanted the type of mat that has the pointy knobs on the bottom so it doesn't slide all over the floor. This works great and the price was reasonable.
After the first time I sat in the chair in front of my computer the chair left notches in the surface of the chair mat. I guess I should have gotten a mat with a harder surface.