ORIGINAL: Jim Dines
On thinner plastics, I generally run the drill bit in reverse. It is slower, giving you more control and doesn't tear the plastic as a forward drill might. On thicker plastic, I start out with a reverse cut, then go with a forward cut after a hole diameter has been established. I use a backing material when drilling plastic so as to allow drill pressure wthout damage.
I use dental burrs and not drill bits. You can buy small burrs at your local dremel supply store. Normal drill bits tend to rip plastics and fiber glass apart.