Cut a square around the damage. You can do this with your utility knife by cutting a little at a time, but a keyhole saw or handheld oscillating saw works better.
Whenever you cut into a wall, make sure to avoid wires or plumbing.
Cut two pieces of wood that measure bigger than the top and bottom of the hole. Put the wood inside the wall, with half hidden so you can screw through the drywall into the wood.
Measure the square hole you just cut. Subtract a quarter of an inch from the width and height, and cut your new piece of drywall to these measurements. Place the piece in the hole and attach it with drywall screws to the scrap wood.
To cut drywall, you score a line in the paper coating across one end. Flip the piece and hit it, so it pops and folds open, then cut the paper on that side. For example, if you need an 8-by-13-inch piece, first score an 8-inch line all the way across the end, pop it and cut it off. Now you have an 8-inch by 4-foot piece, so score a 13-inch line on the cutoff piece, and so on.
Fill your mud pan. If you’re using a powder, rather than pre-mixed mud, mix it with water without making it too soupy.
If you’re using mesh tape, stick it over the seams first. Then apply the compound.
If you’re using paper tape, first spread the compound over the seams. Then cut pieces of the paper tape about as long as the seams and smooth them into the joint compound with your drywall knife. Press hard, as you want the tape to press flat into the mud.
Paper tape is firmer than mesh and better for corners. Mesh tape is better for high-moisture areas and sticks to the wall, speeding up the patching process.
Typically, two more coats of joint compound will secure the drywall. Wait until the previous coat is dry, and before applying more, scrape flat any ridges in the previous coat.
Each coat should spread out further than the last to help hide the bump. For the third coat, spread the joint compound on each side of the seam, rather than just over top.
Don’t leave mud in your pan in between coats. Clean it out with water from a hose or a bucket. Also, trying using a fan to speed up the drying process.
When dry, sand the joint compound flat in circular motions. Be sure to flatten it against the old wall to avoid lines.
If the wall is in an unfinished room or garage, you’re finished. If not, paint over the patch with primer.
If you see any bumps in the patch after priming, you might need to do another coat of joint compound. When it’s primed, paint wall color over the patch and an additional foot on each side in order to hide the patch.