Thanks to George, Sonja, Chad, Ian and Andy.
When you exit the arrivals terminal, just walk ahead for about 3-5 minutes or so and you'll run into a big parking lot with buses. You can ask the people around you and they should be able to direct you.
Note that this is if you arrive in terminal 1 (the newest terminal, where most international passenger flights seem to come in). If you arrive in Terminal 2 (the old terminal), I read in the Lonely Planet that one bus picks up there (though I'm not sure exactly where) until midnight, and the other all night. The transfer bus from one terminal to the other is very well marked now! It seems to run all night, to boot (or at least until 2 or 3 am).
The easiest way that I've found to find bus stations or get help when at the airport or similarly touristy areas is the following: find a taxi driver (or anyone really) and indicate that 5 pounds is all you have to spend, and that you need to get to downtown. Taxis won't even take you from one terminal to the other for 5 pounds, so having already lost you as a potential customer, they will tell you where the bus is.
Also, if you want to take the bus from Abd el Moneam Riyad or Ramses, you may have to get off early (likely when a bunch of other people get off) at a central area where the transfer buses stop and hop on a transfer bus to the proper terminal. I asked the driver, and then asked him again when people hopped off - it worked out.
Added on 9 Oct 08: Check the Cairo airport website on http://www.cairo-airport.com/services_transportation.asp for more details.