Civilization Stage plays out like a strategy game; your goal is to control cities, and you can seize them militarily, convert them religiously, or use economic power to purchase them. Money is generated by cities (the more factories in a city, the more money it generates) as well as by seizing and controlling spice nodes. You can spend money on constructing buildings as well as an assortment of land, air, and sea units that you can design in the various vehicle editors. Or, if you want, you can just go to the Sporepedia and select buildings and vehicles that others have made.
IGN: Spore Civilization Stage Video Preview