Is it possible to use the Apple remote to control Keynote presentations? How so? I have a mid-2010 white plastic unibody MacBook. (I've been told that this isn't supported, but perhaps there are third party solutions.)
Yes - although most people are using the iOS based Keynote Remote these days, the old infrared (which is very thin / physically touchable and very reliable in dark rooms and easily hidden in a hand) works just fine.
The Keynote '09 help shows what functions the various buttons will perform when you are in the various modes: Keynote window itself, presentation mode and slide switcher mode.