Cut out the area of the wall that is damaged. Use a jigsaw and try to make a fairly basic shape such as a square or rectangle. Ensure that the section you remove stops in the middle of the width of studs so you have a place to attach the new piece.
Pry the drywall off of the wood studs carefully with a pry bar so you can keep the piece from breaking.
Place the piece of drywall that you cut out of the wall over a new piece of drywall and trace the shape.
Cut out the new drywall along the trace line. Score the drywall with a utility knife and snap off the edges to get to the shape.
Measure the width between the studs and cut out 2-by-4 boards to go between them. You need to have enough to fit between the studs at the top and the bottom of the new drywall panel. Use a circular saw to cut the boards.
Slide the boards into place between the studs and toenail them to the studs with 3-inch nails.
Place the drywall in the hole on top of the studs.
Drill drywall screws through the panel and into the studs.
Spread on a thin layer of drywall compound over the seams of the new section and apply drywall tape over it.
Cover the tape with a second layer of compound and leave it to dry for 12 hours.
Sand the compound after it dries and cover it with another coat of compound. Let this coat dry and sand one more time. Paint the section of the wall to match the surrounding area.