This game is really fun - a great strategy game for the Xbox
Domination victories are when you capture every capital city in the game. There are 5 civilizations, each one possesses a capital. You have one, and need to get 4 others. This is easily accomplished by a quick blitzkrieg at the beginning, or once you have a substantial amped up nation, a overwhelming force.
Cultural victories are easy to accomplish when you have plenty of culture. Temples, cathedrals, wonders and some great people contribute to culture. Building wonders and getting great people allow you to build the UN to win. Great people are acquired if you research a technology first, if you have a certain amount of culture, or if you take them from other nations. Different forms of governments contribute to culture, or don't. What government you have can help you win a particular victory.
Economic victories are accomplished by gaining a lot of money. Cities gain money every turn, but to win, you need a lot of cities, and banks in each city. Building the great bank after acquiring all the money needed wins you the game.
Technology. Researching a new technology gives you all sorts of benefits, but when you research 48, you can launch the alpha centuri craft, to reach another world. When it reaches another world, you win. You research technology by acquiring a certain amount of science every turn. This is controlled by the size of your city, and if you have libraries and universities.
All in all, the amount of different scenarios, civilizations (there are 16), different ways you can win, and altogether fun of it makes this a great game, although the somewhat poor graphics of your armies and stupid noises they make flaw an otherwise perfect game.