Cut away the rotted drywall. Use a utility knife and cut through the drywall. Keep your cuts square to make it easier to fit in the new panels. Cut away any drywall that appears damp as well.
Cut the new drywall panels to fit. Measure the size needed to fill in the hole. Cut your new drywall panel using a utility knife and a straight edge. Make the first cut, and fold the drywall panel to break it. Cut through the paper with your utility knife.
Insert the new panel. Fit the new panel into the hole. It should be a nice tight fit. If it's a little too tight, make a small cut using a utility knife to trim it. Screw the panel into place over the wall joists using drywall screws. Place a screw every 12 to 18 inches.
Tape over the joints. Use a self adhesive drywall tape and cover all the joints.
Mud over the joints. Apply drywall mud over the tape with a trowel. Smooth this out and let it set. Sand it with a medium grade of sandpaper until the surface is smooth.
Prime and paint the patch. Use the same primer and paint as you did for the original wall. Prime it, wait for that to dry, and apply the first coat of paint. Let this dry and apply a second coat if needed.