The process for repairing drywall often depends on the size of the hole or crack. For smaller holes that are caused by nails or screws popping back out of the drywall, simply push the nail or screw back into the drywall and apply drywall compound to the divot to fill it.
Far larger holes, use wire mesh to make the repair process easier. Place the wire mesh over the hole. Mesh is thin enough that it does not mar the surface of the wall. Tape the edges of the mesh against the wall using paper or drywall tape. Then, using a trowel, apply drywall compound over the tape and the mesh to cover the hole. After the compound has dried, sand it down with fine sandpaper to hide the hole.
Larger holes can also be patched using a wood backing and a new piece of drywall that is cut to size. In this case, it is important to cut a square around the hole using a drywall knife before securing the wooden backing to the backside of the drywall. Once the wood backing is in place, cut a piece of drywall so that it fits into the square hole. Secure it to the wood backing using drywall screws, and frame it using paper tape. Next, apply a coat of drywall compound to the patch to blend it into the surrounding drywall.