To drill Plexiglass correctly, lay it on a piece of scrap wood, mark the target area, make a pilot hole, and drill the final hole. This process requires scrap lumber, a grease pencil, masking tape, a drill and two plastic-cutting drill bits. You also need a spray bottle, water and clamps.
Lay a thick piece of scrap lumber on your work surface, and put the Plexiglass on top of it. Secure the Plexiglass with clamps. Mark the target area with a grease pencil, and cover the mark with a small piece of masking tape.
Select a plastic-cutting drill bit approximately half the diameter of the finished hole, and attach it to the drill. Drill a pilot hole through the masking tape. Keep drilling until you feel the drill bit enter the scrap wood underneath the Plexiglass.
Extract the drill from the Plexiglass, remove the bit, and attach a bit that matches the desired diameter of the finished hole. Fill a spray bottle with water.
Drill into the pilot hole, stopping often to spray the bit with water. This lubricates the bit and cools the Plexiglass, preventing melting. Failure to cool the Plexiglass causes it to overheat and melt, enlarging the hole. When you feel the bit break through the Plexiglass and enter the underlying wood, turn off and extract the drill.