These problems used to plague multiplayer and were patched. Make sure your LAN/Internet settings from a router/modem are fine.
If all else fails I would highly suggest purchasing the expansions to play the game with Gods and Kings or Brave New World. There is lots of balancing that occurs that Firaxis did not patch into non-expansion Civ 5. I hate to support laziness on behalf of the developers/publishers but the fixes are worth it if you intend to play.
Now for the bad news, sadly all Civ5 games seem to deteriorate over time. The game simply cannot handle itself and late games always turn to lagfests riddled with disconnects, bugs, and glitches. My advice: SAVE, SAVE, SAVE. Save every few turns to save yourself nightmares and every 30-50 turns I suggest creating a new save file to keep an archive of the game. I have experienced save files becoming corrupted and unusable for in-explainable reasons. One certain reason was after a patch. Patches frequently corrupt save files.
Despite all of that, the game is still amazing which is why I play it. My normal configuration is 2 player MP on huge maps with exactly 7, 8, or 9 AI. (Whatever the # is w/out the WARNING).
Turning off settings like Unit movements and automoving cameras have increased our game's stability as well as made the game faster.
Hope this helps somewhat. Best of luck in your conquests.