The general strategy that I follow is as such:
1) I always found my capital near two squares that has extra food production and lots of hills; this is extra fast population growth and extra shields.Often this means having to restart the game before turn one has even been completed but its worth it.
2) Next I research pottery and turn the science rate to max; depending on the civ I'm playing with this takes about 12 turns.
3) While I'm waiting for granary to become available I pop out 3 warriors; one stays home as the other two go explore. The one worker that I have available I use for tile improvement around the capitol, obviously.
4) After I've build my granary I get one more worker out to join the other worker; if I'm playing with an industrious civ then this means that together they can have a road finished in one single turn; a great help to have my settlers travel fast to their place of destination as I always construct a road there first.
5) Next I create up to 6 settlers and either have them found a city really close to the capital so as not to have to deal with corruption or at places that have luxuries or iron nearby , only resource that becomes visible that early in the game is iron.
6) After my capitol is finished producing settlers I let it produce a temple and next have it start building on a wonder.
7) Same goes for another city that is locates near my capitol and thus has little corruption; I found out that this is the only way to beat the other civs to pyramids and oracle.
8) I let another city that has a good food production rush build a granary and then pop out as many settlers as I can.
9) Yet another fast growing city is used to produce workers; depending on the civ I'm playing with, mostly either the french, persians or egyptians for the simple reason that I think that 'industrious' is the best deal you can get with civs, this means you only need one turn for two workers to finish that road that I'm most concerned about early in the game; connected city's that have access to luxuries don't revolt half as easily as unconnected cities without access to luxuries do, plus having a settler travel to its destination by road takes 3 times less time then without the road and often this has allowed me to arrive in time just before a rivaling civ got there. Another good reason to be concerned about roads is that shield/food producing tiles+roads=extra gold per turn.
10) Two other fast producing cities are set to build a barrack and then start spitting out spearman; I want at least one warrior, later upgraded to swordman if I can get Sun Tzu's Art of War, and two veteran spearman guarding each city this early in the game; bordertowns that run the risk of being attact first are guarded by at least one warrior and four veteran spearman.
11) After I claimed as much land as I could or was strategically possible; I hate having to deal with city's that only 'produce' corruption and so unless there is a resource or a luxury I never found cities too far off from either my capitol or my forbidden palace, and have them well guarded I first let them build a temple, temple=culturepoints=territory, next I have them build a library and a marketplace; after that its just keeping up with whatever new improvements become available.
12) Throughout the game I have a fast producing city set to build palace only to switch this when a new wonder becomes available to be build.
13) Wonders that are absolutely essential in my opinion: Pyramids, Adam Smith's Trading Company, JS Bach's Cathedral, Leonardo's Workshop, Michelangelo's Chapel, Sun Tzu's Art of War, Hoover Dam and Universal Suffrage.
14) Science rate is set at max throughout at least the early eras; after that depending on my max income and the luxuries that are available for trade/wanted by other advanced civs, I might lower my science rate in favour of more gold per turn so that I can buy-trade for science advances.
15) One thing I learned to avoid is to have a mutual protection act with any other civ; having one is setting yourself up for war with any other given civ without knowing in advance which civ that will be..
15) I only declare war if I know that I have absolute militairy superiority over the civ that I'm about to wage war on; and while invading enemy territory I always leave enough troops home to defend my own cities in case I get to deal with an invading third civ who just signed an mutual protection act with the civ that I'm at war with and hence declared war on me..
