Remove the door from its hinges by driving the hinge pins up through the bottom of the hinge with a hammer and screwdriver. Start with the bottom hinge and work up to prevent the door tipping. Lay the door flat on a pair of saw horses.
Sand the affected area with 150-grit sandpaper on a random orbit sander. Include the area directly surrounding the damage, as well.
Fill any dents or dings in the door with solvent-based wood filler for stained doors or body filler putty for painted doors. Use a flexible putty knife to spread the filler evenly into the damaged area, leaving it raised a bit from the face of the door. Allow the filler to set for 30 minutes.
Sand the area smoothly with 150-grit paper. Wipe the dust from the area with a rag dampened in mineral spirits.
Apply two coats with a soft bristle brush of matching paint or a coat of matching stain/finish all-in-one to the damaged area. Paint in long straight strokes, working with the grain on wood doors or vertically on smooth-faced doors. Wait the manufacturer's recommended time between coats and before rehanging the door.
Rehang the door by aligning the hinge halves and driving the pins downward into the hinges, starting with the top hinge.
Remove the screws from the jamb-side hinge plates with a cordless drill. Start from the bottom and work your way up. Lay the door flat on a pair of saw horses.
Tighten any hinges that are loose in the edge of the door with a screwdriver. Replace stripped screws with screws 1/2-inch longer than the original.
Drive the hinge pins out with a screwdriver and hammer to separate the hinge halves. Replace the jamb-side plates into the mortises in the jamb. Drive one 3-inch screw through each hole in the hinge plates through the jamb into the frame behind to anchor the hinges.
Stand the door upright. Align the hinge halves and drive the pins down into the hinges from the top, starting with the top hinge and working down.
Test the door for proper operation. Correct any sag by tightening the uppermost screw in the top hinge with a cordless drill to lift the door slightly. Tighten the remaining screws accordingly.