Draw a neat and even square on the wall around the hole with a pencil, and cut the square out of the wall as neatly as possible using a small saw or knife. Handle the cutout carefully so it doesn't break.
Trace the cutout piece of wall on a piece of plaster board, and trace a 2-inch-wide frame around the traced square to mark the location for cutting.
Cut the traced piece from the plaster board, and remove the paper affixed to one side of the board.
Remove the plaster from the frame area that was traced around the plaster patch. You will have a plaster patch that has a 2-inch paper frame.
Apply patching plaster around the edges of the hole in the wall and around the edges of the plaster patch. Use a putty knife to apply and smooth the plaster.
Place the patch over the hole in the wall, and press the paper frame in the plaster. Hold the plaster patch in place until the patching plaster sets.
Sand the edges of the plaster patch lightly with sandpaper, and paint the patch to match the wall color.