It's good to get your cities up to 31 in population because you can get 248 science or gold production without a market, bank, library or a university plus you'll have 1 production per 1 population number thats 31 production and that would be doubled if you built a factory.
When making a good defensive unit make a modern infantry army and get lots of victories then when you have a defensive strength of 144 build some walls that will change it to 168 then build a veteran battleship fleet and then you have 225. Next build SDI defense and now you have an unbreakable defensive unit this is especially easy to make in the Beta Centauri Scenario.
When finding it hard to win an economic, cultural, domination victory go to single player menu and select "play scenario" and the select beta centuari you start of on start different planet which looks excactly the same as earth and the good thing is you and unfourtunately you're fellow civilizations aswell have all technologies so you can build a market and a bank straight of or a temple and a cathedral and artillery, tanks, battleships, modern ifinatry and spitfighters and all the others. Plus all the wonders are available for your needs.
When playing as Cleopatra in Cheiftain diffuculty overtake the Romans as soon as possible if you want a domination victory. But even if you don't it will still give you an extra city and help towards other victories.
When you are looking to destroy a heavily defended strong city that you have to destroy to get to the capital here is how you don't just kill the warriors there but how you blow it up and leave no trace off it. It's simle survive and fcomplete the reaserch for the manhattan project and you'll get a weapon 800 times as strong as a atomic bomb.
When your trying to win the game domination style get the horse quickly as they are strong in ancient times as the other civilizations don't use them hardly before 1000AD plus they are very strong like two horsemen can have the average attacking power of eight which can take out your average warrior army but a bigger reason is because they lead to knights which can become invunrable
When you have the chance to build the Oracle build it as it will tell you wether you will win the battle or not but if you attack with there defending unit only being a point or two over you choose to retreat and they'll grow stronger but die and they unit will weaken it up to you by the way this is of a demo version but it may work try it out.