Place a drop cloth on the floor underneath the hole in the wall. This protects the floor from drips or splatters of drywall compound.
Peel the backing off a peel-and-stick aluminum patch covered with fiberglass mesh. Put the patch over the hole in the drywall so it's completely covered. Press the patch firmly in place.
Use a putty knife to apply a thin coating of drywall compound over the entire patch. Follow manufacturer instructions on the drywall compound label. Extend the compound approximately 1/2 inch past the edges of the patch.
Use a 12-inch drywall knife to smooth out the first coat of drywall compound. There should be no indents, lines or thick areas.
Allow the drywall compound to dry completely per manufacturer instructions. Apply two more coats in the same manner as the first. By the last coat, the peel-and-stick aluminum patch should be completely hidden.
Lightly sand the repaired area of drywall to make it smooth. Paint the drywall compound so it blends in with the surrounding wall.