Mark out a square border around the wet area with a level and pencil. Position the two vertical lines so they are along the inside edge of the wall studs on either side of the wet area. (Find the positions of the studs by pulling away part of the wet wall material to get inside it, as needed.) Put the two horizontal sides at 3 or 4 inches above and below the wet area.
Cut out the square, using a jig saw. Both vertical sides of the new hole should be lined up with the inside edges of the wall studs
Use a screw gun and 2 1/2-screws to affix 2-by-2-inch boards to the sides of the studs, with the forward-facing edges of the boards even with the front edges of the studs. The 2-by-2s should be set back from the surrounding drywall or plaster.
Put one of the plywood scraps inside the hole and hold it along the top span, with about half the width of the piece back behind the wall and the other half projecting into the hole so it's visible from the front. Secure the pieces with 1 3/4-inch drywall screws shot through the wall along the top and into the plywood behind it. Repeat the process to install the second piece of plywood along the bottom span of the hole.
Measure the square hole. Transfer the measurement to a piece of wetrock. Cut the drywall by scoring it with a utility knife and snapping it at the line.
Press the wetrock patch into the hole, with the back of the piece resting against the boards. The face of the wetrock should be even with the surrounding wall. Shoot drywall screws through the wetrock and into the boards behind it, putting screws every 6 inches or so.
Press drywall tape over the perimeter of the patch. Spread joint compound over the drywall tape with a drywall knife. Make it smooth and flat.
Let the compound dry for about six hours. Spread on a second layer. Let it dry. Spread on a third layer. Let the third layer dry for 12 hours. Sand the patch flat and paint.