Inspect the wall to determine the extent of the damage. If the wall has a deep indentation or a portion of it is completely gone, cut out the section with a drywall knife to form smooth, straight edges. Cut out the section so that wall studs are visible on both sides. You'll need these to attach a new piece of drywall.
Measure the opening with a tape measure and cut a new piece of drywall to fit, using a drywall knife. Score the board on both sides and snap it to remove a piece.
Fit the drywall to the opening and attach it by drilling drywall screws into the studs.
Spread a thin layer of drywall mud along the seams between the new and old drywall and press drywall tape into it. Once the tape is down, spread another layer of mud over it. This is also what you would do if the damage is relatively minor. Simply spread a little mud over the damaged area and feather it out. Let the mud dry for a day.
Sand the surface of the drywall mud to smooth out any roughness. For taped areas, apply a second coat and feather it out away from the tape. Let it dry another day.
Lay down a dropcloth and paint the repair to match the rest of the wall, using a paintbrush and painting with long, even strokes.