1. Don't remove the protective film until you have finished all work on the piece. I know it can be very tempting to take a peak when you've tapped that first hole but you need to keep as much protection as possible until you have completely finished the piece.
2. Cover the whole piece with strips of masking tape (the wide stuff 50mm) before you start. This has two benefits. Firstly, the tape adds an extra layer of protection against scratching. Secondly, the masking tape can be used to mark out your drill/cut points.
3. Clamp your work down. When drilling a loose piece of Perspex the piece can be lifted off the work surface by the corkscrew effect of the drillbit. Trust me, this happens and tends to make a real mess. Use cardboard to protect the Perspex from the clamping surfaces especially if those surfaces are knurled. The knurling pattern will imprint on the Perspex if you don't.
4. When drilling place your Perspex on an offcut of flat wood. This prevents the drill bit from suddenly breaking through the back of the Perspex and snapping chips off around the edge of the exit hole. If it's placed firmly on a piece of wood the exit hole should be as clean as the entrance hole.
5. Use a slow RPM with a good sharp drill bit. I have had best results using good quality HSS drill bits. Blunt drill bits or too high RPM will melt the Perspex rather than cut. Drill a small distance then retract the bit and clear the swarf. If you try to drill too far in one go you risk clogging the flutes and overheating the Perspex. I found that you can smell the plastic as it starts to heat up, a good indication that the work is getting too hot.
6. With the work held firmly (see point 3) using a taper tap start threading keeping the tap perfectly inline with the drilled hole. Once in a few threads the tap should hold itself inline with the hole. I usually back out completely at this point to clear the tap flutes. Present the tap again and rotate till you start to feel the tap cutting again. I find its best to cut one full rotation then back at least one full rotation then forward till you feel the tap start to cut again then one full rotation and so on. If it starts to require more effort to cut it's time to back all the way out again, the extra effort means the flutes of the tap are full of swarf and/or the work is beginning to heat up. If you allow the work and tap to heat up the Perspex will just melt and the threads will not cut clean. If you are tapping a blind hole you may need to remove swarf that drops to the bottom of the hole, this can be done by removing the work from the clamps, inverting and poking out with a small impliment. Another way is blasting it out with a tin of compressed air. Again, if you are tapping a blind hole, you may need to swap to a bottoming taper so you can cut the threads all the way down to the base of the hole. A good tip is to use a glass of water to cool the tap everytime you remove it from the work. Also a small wire brush helps remove swarf from the tap everytime it's removed from the work.
