Hey folks, GalCiv 1 junkie, first time poster...
To the point: I've found that I can quickly win a game by following this formula...
Create a construction ship with two warp drives and a construction module on a cargo hull, crank 'em out as fast as possible. While building and fortifying starbases in enemy territory I research the culture tree, and then install the culture modules in appropriately-fortified bases. The AI declares war and tries to pop the influence stations (way points to each station are, of course, named "culture bomb 1," "culture bomb 2," etc). AI backs off after the solar system flips. Rinse, repeat. Just make sure you got the dough to pay for the uber culture modules, and you're set.
Too easy? How should the AI adapt?