Cut away any splinters or ragged edges with a sharp utility knife.
Insert a small amount of spray foam insulation inside of the hole. Spray foam expands quite a bit once it dries, so a little goes a long way.
Cut away excess foam insulation once it dries. Drying time is usually about fifteen minutes. Slice off the excess with the utility knife.
Apply enough wood putty to the repaired area to cover the foam. Smooth it against the door with the putty knife, lightly scraping off the excess with the edge of the knife so that the putty is smooth and flush with the door.
Sand the repair smooth with sandpaper after it dries. Clean away the sanded particles with a tack cloth.
Stain or paint the door as desired.