I've been reading about GOTM in the Civ II Forums. Should I take it to mean that everyone starts with the same map/settings and then everyone tries to do their best on that map? Are there any other rules? I think a re-post of the rules for GOTM would be a good idea for this forum.

That's pretty much it. Except for the fact the score was measured in a different way.

No cheating is another rule. This refers to the Save/restart when ever something bad might happen. No map editior during the game and such.

You can find more info about GOTM as well as results for past GOTMs in the Game of teh Month section:

http://www.civfanatics.com/civ2gotm.shtml