Set a ladder underneath the patch. Lift a level up to the ceiling and place it next to the patch. Draw a pencil line down the level. Move the level to the patch's other side and draw another line. Use the level to draw two more lines, forming a square around the patch.
Poke a drywall saw's blade through one of the square's corners. Use a sawing motion to cut along the line and then pull the blade out of the ceiling.
Insert the drywall saw blade into the square's corner opposite from the corner you started from in Step 2. Cut along that line and pull the blade out.
Push the drywall saw's blade into a third corner and cut along the line. Use your hand to support the patch square, since now it is free from three sides. Use the drywall saw to cut through the fourth and final line.
Lower the patch from the ceiling. Measure the square opening's length and width and prepare a new patch, according to the manufacturer's directions.