Turn off water to the toilet at the house main. Flush the toilet to empty the tank of water. Use the adjustable wrench to loosen the nuts that hold the tank to the toilet base. Disconnect the water supply line to the tank. Remove the tank and set it to the side.
Use the utility knife to cut away the damaged wall area. Pry the old sheetrock out. Remove screws from studs. Measure the opening. Make marks on the remaining wall to indicate where the studs are, which will save you time later.
Cut a sheet of drywall to the correct size. Place the drywall into the opening, and screw it into place with the drywall screws. Install the screws so that they dimple the drywall without tearing through the paper.
Place mesh tape over the seams of the new panel. This tape is slightly tacky and will hold in place on its own for short periods of time. Load up a tape knife with joint compound, also known as mud, and set a layer of this mud along the tape.
Holding the knife at an angle, scrape it along the freshly laid mud so that the tape is covered and the mud is smooth. The mud will extend past the edges of the tape. Mud over the screws also. Set mud over the screw and scrape away the excess, leaving a flat surface behind. Let the joint compound dry completely. This can take anywhere from 4 to 24 hours, depending on the type of joint compound chosen.
Sand the area smooth. If the tape shows through, add another layer of mud. Let that layer dry, and then sand it smooth again. The area is now ready for paint or other wall treatment.
Reinstall the toilet tank. Set the tank back on the toilet base, and reconnect the water supply lines. Install the tank bolts and nuts. Do not over-tighten any of these connections, as the tank or plumbing lines may get damaged. Turn the water back on.