The Virtues of Drywall
Drywall has been the wall finishing material of choice for most of a century because it's so easy to install and finish. Another of its virtues is that when it's damaged, it's easy to repair. For scratches or small dents, a quick swipe of joint compound with a 3- or 4-inch putty knife and a bit of sanding before priming and painting will do fine. For small holes up to 3 inches, self-adhesive plastic mesh tape and then a coat or two of patching compound will work. For medium-sized holes between 4 and 6 inches, try a drywall bandage.
Check to make sure there is no electrical wiring in the area first, then use a keyhole saw to cut the hole into a neat square or rectangle. Transfer that shape onto a piece of new drywall, add 2-inch margins and cut out the larger patch piece. Trim off the back and gypsum in the 2-inch margin but leave the face paper uncut. Spread patching compound around the outside edges of the hole and press the bandage into it, feathering the edges. Let it dry. Then sand and re-coat with compound. Finally, sand again, prime and paint.
Patching Large Holes
For really big holes, you can use the tie and twist bracing method. Cut a piece of drywall or a length of 2×4 a few inches larger than the hole. Drill two small holes in the center and loop a 2-foot string through it like a button. Tie the ends around the middle of a stick. Apply adhesive to the back edges of the hole inside the wall. Adhere the patch piece and twist the stick from your side of the wall until it holds tight. Then, fill the remaining space with drywall patch pieces and mesh tape. Finish with compound as usual, cutting the string and pulling it out just before it dries.
Patching Super-Size Holes
For super-large holes bigger than a foot wide, cut the drywall back to the two nearest studs and expose them halfway. Cut a new panel of drywall to fit and attach it as you normally would with drywall screws, joint compound, and tape.