The following method will work to fix large holes of a couple feet or more in walls and ceilings. This repair process requires the use of added wood framing to hold the new drywall patch in place. To repair smaller wall holes of several inches, without adding framing try this process.
Use a piece of drywall the same thickness as the wallboard. Cut a piece a bit larger than the damaged area and hold it over the hole to mark the pattern on the wall.
Use a drywall saw to cut from inside the hole, out to each corner of the square. Cut a bit past the pencil mark at each corner to be sure the new piece of drywall will fit easily without forcing.
Score the pencil lines around the hole with a sharp drywall knife. Cut just a bit outside the lines to keep the squared hole large enough for the new patch to fit easily.
Snap the wallboard pushing it into the hole along the score lines. Cut completely through to the paper on the back side of the wallboard and remove the damaged pieces along each side of the squared hole.
Hold the new drywall patch in place to check that it fits into the new hole easily without being forced. If necessary, trim around the edges while holding the patch in place to remove any obstructions that prevent a good fit.
Measure the opening of the squared hole and cut two furring strips, 6 inches longer than this measurement. Hold each board against the squared hole and mark it with a pencil to indicate the edge of the hole. Make the mark so it will be visible when the board is held against the inside of the wall.
Insert each furring strip into the hole, and using the marks for positioning, attach them using using drywall screws and a drill-driver. Hold the wood, pressing it tightly to the inside of the wall and drive the screws through the surrounding wall and into the strips at top and bottom. Sink the screw heads just below the wall surface.
Place the new piece of drywall over the new framing and attach it with screws. Use at least 4 screws, one at each corner and sink the heads below the surface of the drywall patch.
Cover the seams around the new patch with fiberglass mesh tape. Overlap the ends at each piece of tape at the corners.
We use a 30 minute setting-type joint compound for the first two coats of this repair. The third and final coat is made using ready-mixed compound for easier final sanding and a smoother finish.
See the these instructions to mix up a pan of setting compound and use a 6 inch joint knife to apply a first coat. "Butter" the surface with a thick coat that covers the tape and the surrounding surface.
Immediately go back and skim off the excess mud to leave a semi-rough coat behind. Go over it a couple times to remove most of the mud. Don't try to hide the tape or level out the wall with this first application, it will take a couple more coats to build up a smooth, level surface, just use this coat to stick the tape down.
Let the mud set until it is dry to the touch and then lightly sand the tape with medium grit sandpaper. Go easy to just knock off any mesh fibers and ridges in the mud, don't dig into the fiberglass with the sandpaper. Wipe off the dust going over it lightly with a damp rag.
Mix and apply a second coat of setting compound. Use a wider joint knife this time to spread a thick coat over the whole patch. Immediately go back over it to skim off the excess using parallel strokes from one side to the other. Try to make the mud level with the surrounding wall as much as possible, but don't let it protrude past the wall level. Ignore any ridges left by the edge of the blade between strokes, you can knock them off before applying the next coat. Allow the mud to set until hard.
Scrape off any ridges from the joint knife using an upward stroke to cut them off. Sand if necessary to remove any other roughness and wipe off the dust. Apply a third coat over the whole patch using ready-mixed joint compound. Use the same method of applying a thick coat first and then skimming off the excess to smooth the mud. To aid in getting a level surface, stroke in the opposite direction of the previous coat. If you skimmed the mud horizontally before, skim with vertical strokes this time.
After the mud dries apply another coat, if necessary, to fill any scratches or pits in the surface, don't try to sand these out, you'll make the surface uneven. If another coat is needed, sand lightly, wipe off the dust and apply the mud going perpendicular to the previous coat.
Allow the final coat of mud to dry completely and then sand the whole area. Use medium sandpaper to sand the patch and feather the edges into the surrounding surface.
Wipe away the sanding dust with a damp rag and touch up the paint over the repair. If you are using flat latex finish paint, it will be self-priming. If you are using semi-gloss or other shiny paint, prime the patch with flat latex paint or a latex primer before touching up the finish.