A real, traditional Full Moon Party (or rather, FMR - for Full Moon Rave) is an underground party that takes place in a remote, unadvertised location, usually fueled by word-of-mouth. Generators, equipent, and other party-ish things are brought, and loads of people just go all-out and have themselves a little party in the middle of nowhere - generally with no rules, but just an ingrained respect not to be anti-social toward anyone else. Obviously, they heppen during a full moon. First off for the paganistic ritual for it, secondly because in remote areas, the moonlight helps you find your way to the oft-secret location.
'Course, in this day and age of commercialized culture, a real FMR is hard to come by. You'll find "Full Moon Parties" advertised all over the world on flyers, in record stores, etc. There was a thread about these in Thailand, where masses of youth go to party, even though it may not even be a full moon. In researching my trip to Australia, I found that some of the bigger megahostels also host monthly Full Moon Parties, basically a big ol' beer bash with a DJ or two... It's now become a bit of a marketing phenomenon, as well as an excuse to get a bit wilder than usual.. I'm not knocking it - they're still a ton of fun - but you shouldn't confuse these with the underground FMRs of yore.
You can find out about them in whatever area by doing, for example, a Google search including the area (say Washington DC), "fmr" and "rave." Best way, of course, is to get into the party scene and hear by word of mouth. Enjoy!