Multiplayer games can be very different from singleplayer games; this article should help you find multiplayer games, learn common practices, and how to handle problems.
You have three options for finding games: BattleGoat Studios' "Multiplayer Games" forum, the Supreme Ruler 2010 Gamespy Arcade lobby, and the #sr2010 IRC channel. There are usually few or no people just loitering in Gamespy and IRC, but they can be used to meet for a game posted on the forum. If you post on the forum, you may want to do so at least a day or two before the game.
These are some common practices in multiplayer:
To rejoin a player who has disconnected, you must distribute a savegame to all players and restart from the multiplayer lobby using this savegame. Savegames can be over 5MBs in size uncompressed, but in a ZIP archive they will be only a few hundred kilobytes. All players should have the uncompressed .SAV file in their "Supreme Ruler 2010\Savegame" folder.
Repeated sync errors can have no apparent effect, or put players on very different versions of the same game. Wish we knew how to tell. If you think the sync errors are trivial, then having everyone press CTRL+S will turn off the default pause. Otherwise, try loading from a savegame.