If you have a hollow-core door with a serious hole in it, consider replacing the entire door; hollow-core doors are modestly priced.
You can repair a hole if you're willing to paint the door to hide the patch. To do this, you'll need a can of spray foam insulation. In many cases, you can repair the door without removing it first--just spread a dropcloth on the floor beneath it before you start.
1) Fill the hole with the spray foam insulation, allowing the foam to expand slightly above the door's surface.
2) Let it dry (and continue to expand) overnight.
3) Use a razor blade to slice off the excess. Shave the mound just slightly lower than the door's surface.
4) With a 3-inch putty knife, apply vinyl spackling compound to the patch and draw it smooth to the door's surface. Allow the spackling compound to dry.
5) Sand the area lightly with fine sandpaper.
6) Prime the entire surface of the door, allow to dry, and then paint.
