Open the door. Insert the latch into the hole in the end of the door until the latch plate is resting against the surface of the end of the door. Trace around the outer circumference of the latch plate with a pencil onto the door. Make pencil marks through the screw holes in the plate onto the door. Remove the latch and place it aside.
Use a 1/8-inch drill bit and a power drill to drill shallow pilot holes through the end of the door on the pencil marks indicating the latch plate screw holes.
Position a wood chisel so that it is perpendicular to the end of the door, and the sharp edge is resting on the latch plate outline. Ensure the flat edge of the chisel is facing away from where the latch will be and that the beveled part of the chisel is facing the latch. Tap the end of the chisel with a hammer so that the blade penetrates the door to a depth that equals the thickness of the latch plate. Continue around the entire outline in the same manner.
Remove material from within the outline by placing the chisel at an angle with the beveled edge flat on the surface of the door and tapping it with a hammer. Ensure you do not cut deeper than the thickness of the latch plate.
Use the chisel by hand to clean the corners and the bottom of the recessed area as necessary for the latch plate to fit within the recess. Test fit the latch to ensure the latch plate fits within the recess and is flush with the surface of the door.