How should I remove carpet in preparation for sanding and polishing floorboards?
Pull up the edges around the perimeter, roll up the carpet and dispose. If working yourself, cut the carpet into manageable sections you can carry.  There might be padding under the carpet but its probably not tacked down.  Cut and roll it up too.

Use a small pry bar to pull up the tack strips and make sure to remove or hammer down any nails that are not sitting flush with the floor.  If there are stubborn nails, place a small scrap of wood under the pry bar so that you don't damage the floor.