The process to fill holes in walls depends on the size of the hole. Use joint compound to fill small holes, like those left from nails or screws. Use a drywall repair kit to repair larger holes up to 6 inches. For even larger holes, replace portions of the drywall before proceeding with the repair.
Repair small holes
Fill the hole with a small amount of joint compound, using the putty knife to feather the edges of the patch. Sand the patched area so it's smooth with the surrounding surface. Use touch-up paint to cover the patch so it is no longer noticeable.
Bridge larger holes
Holes over 1 1/2 inches in diameter require installing other materials to provide a surface for the patch to adhere to, according to This Old House. Repair kits provide galvanized metal and fiberglass mesh to hold the patch in place. Follow the manufacturer's directions to apply the patch. Once it's dry, sand and paint the patch to match the surrounding wall.
Replace drywall for large patches
For large holes, cut the area surrounding the hole so the edges are even. Install 1-inch lumber behind the wall and attach using drywall screws. Allow the lumber to overlap the hole to provide a place for attaching the drywall. Insert the piece of drywall, cut to fill the opening, into the hole. Use joint compound and drywall tape to fill joints. Finish the joint and paint and create an invisible patch.