You cant - there is no multiplayer option in GalCiv - and at present its highly likely it will stay that way. If you are a multiplayer fan and want background on that go to the GalCiv part of the forum and you'll find a Sticky Thread "The Case for No Multiplayer", its not far off 500 posts long.....
There is a system called the "Metaverse" where you submit games into a "quasi-league" structure. Recently that evolved into another, additional, system, look out for posts re "Metaverse League Round "X", where X= the latest round in the current game series.
Regards
Zy