In the beginning of Civilization stage, your tribe morphs into a city and you become the first civilization (a nation) on the planet. As the game progress, other tribes quickly advance to civilizations and you have to interact with their cities.
The specialization of a particular civilization (and that of its first city) depends on the tribe's nature. A Friendly tribe becomes Religious, an Industrious one becomes Economic and an Aggressive one becomes a Military city/civilization. Be aware that these specializations differ from the Religious, Economic and Military traits the player can gain after completing Civilization stage!
Religious civilizations
A religious city.
Religious civilizations employ conversion to make things go their way. In order to win as this civilization, the player must build religious vehicles and send them to convert the city (select the city and click the convert option). When they reach the city, the vehicles will cause entertainment buildings to stop functioning, creating discontent among the citizens of the city, while a hologram of the player's creature will appear singing and preaching, trying to convert the city. As long as the vehicles aren't destroyed, the city will eventually be converted. The player repeats this till he/she has six cities. When this happens the player can then use the Fanatical Uprising option and convert all cities to the player's religion. The Fanatical Uprising superweapon can also be obtained by pressing Control-Shift-C and entering "unlocksuperweapons". This allows the player to continue to the Space Stage.
Economic civilizations
An Economic City.
Economic civilizations use the powerful Sporebuck to influence other civilizations. The way the player can win with this type of civilization is to establish trade routes with other nations and assign vehicles to man the trade route. Eventually, the player is given the option of buying the city he/she has a trade route with. The player must bid high in order to buy the city or the city might sever the trade route, causing the player have to start over with that city. But if you are successful, the city becomes yours. After you capture 6 cities, you are given the option to use the Global Merger, which buys all the cities for you, allowing you to advance to the Space Stage. The Global Merger can also be obtained by pressing Control-Shift-C and entering "unlocksuperweapons."
Military civilizations
Military city.
Military civilizations use force to get what they want. To win as one of these civilizations, the player must build military units and order them to attack a city. When the vehicles arrive they will begin to bombard the city, destroying all buildings inside; long as the vehicles aren't opposed and can continue to bombard the city, it will eventually surrender. After the player acquires six cities, the player may launch ICBMs to destroy all other cities, allowing the player to advance to the Space Stage. The ICBM can also be obtained by pressing Control-Shift-C and entering "unlocksuperweapons".
Cosmopolitan civilizations
When the player convert/purchase/conquers a city of other specialization than their own, they can choose whether to change it's original specialization. If you choose not to, you'll be able to design and produce vehicles of that specialization (but only in that city). However, the player can (officially) only have one specialization. So if the player does not specialize during his/her gameplay, he/she may want to check which specialization is their official one on the Timeline (by clicking on the button next to progress bar).
Note that Diplomatic takeover is also an option to win the Civilization stage.