Measure the width and height of the opening in the drywall for which you are building the plywood wall panel. Add 2 inches to each dimension to get the exterior dimensions of the piece of plywood you will need. A common size opening for a wall access would be 10-by-16-inches. For this opening, you would need a piece of plywood that measures 12-by-18 inches.
Cut two pieces of 3/4-by-3-inch wood to a length of 10 inches. Cut two more pieces of 3/4-by-3-inch wood to a length of 14 1/2 inches.
Screw the four pieces of wood that you cut in Step 2 together to create a rectangular frame that measures 10-by-16 inches.
Spread a bead of glue around one face of the frame you built in Step 3. Set the piece of plywood on top of the frame so that it overhangs the frame by 1 inch on each side. Secure the piece of plywood on the frame by tapping several small finish nails through the face of the plywood and into the frame.
Fill the nail holes with wood filler. Paint the face of the plywood panel with primer, then with paint to match the wall.
Install the plywood panel over the hole in the wall by sliding the frame into the hole until the panel is flush against the face of the wall.