Ok R1 you're starting to get the idea.
Basically you do well by paying attention to what is going on:
Grow fast in the early game.
Position new cities carefully. For example placing a city by a river means that you can grow past 6 without needing Construction to build an Aqueduct.
Build lots of workers (I like 1 per city) and use them well - build roads to connect every city into your economy, build them in good squares and build mines or irrigation in those squares. As far as irrigation/mining goes, a city with 2 or 3 irrigated grassland squares will grow nice and fast, so once you have those set up concentrate on shields. Make sure your populace is working the squares you improve or you are losing out.
Make good research choices, the AI civs tend to go for techs in a certain order, you've probably figured that by now. When you get a new tech try to trade it with everyone for as much as you can get.
Use your treasury wisely, making gold is the least important aspect of your economy, what you want is science and lots of it, and only as much luxuries as you need to keep your cities calm.
Build the right improvements: Temples are important to expand city radius', which lets you work more squares, expand your borders and prevent cultural conversion. Any city more than half a dozen squares away from yor capital will need a Courthouse or you lose a lot of productivity. Granaries let you grow faster (The Pyramids is a very helpful wonder if you can get it). The benefit of Libraries and Marketplaces is obvious but don't build them until you need to, they cost money to maintain and you could be growing faster instead. Barracks? 1 or 2 can easily churn out enough units to keep your empire safe. when you can build Aqueducts do so, they make your cities bigger and safer, and help your economy grow.
The key is 'micromanagement' - watch every square you use, use every unit of population wisely, build only what you really need, and make sure you trade with the other civs.
