Q&A for How to Drill Plexiglass

There are special drill bits. They aren't "needed," but they are helpful and do a better job.

You'll need a hand saw with a removable blade (like a hacksaw) and a drill bit that is a slightly larger diameter as the saw blade. Sketch the square in the location you want it on the material, then drill into the four corners of the square, taking care to make sure the hole doesn't cross over the square boundary you drew. Next, fit the blade through the hole and proceed to cut along the lines you've drawn. Cut the square a bit smaller than your final dimensions so you can go back with some sandpaper to clean up the cut, and use a sharp blade (use gloves!) to deburr and/or cut a chamfer into the edges.

The trick is to go slowly, use a good sharp bit, and ensure that the section of material you are drilling is supported and will not bend, twist, or otherwise deviate from "flat". You could drill progressively larger holes, but in my experience this can cause chipping around the edges of the hole. Simply drill with the exact size you want, go slowly, and keep the cutting tool as close to perpendicular as you can.

Rotary tools' cutting disks can be very effective, but dangerous due to bind-up / kick-back like on any circular saw.

Any drill bit that is slightly larger in diameter than the widest dimension of the blade (likely just to be the flat side) will work.