Beginning;
In the beginning of a game you will have 1 or 2 Settlers, depending on how the AI assesses your position on the map. You'll get 1 if the AI determines you're in a strong position. Find a map location that has a combination of the following features:
1). Coastal tiles/plains/grassland. Essential for food production and growth.
2). At least one trade good.
3). Not on a swamp
Don't be afraid to look around for a turn or two before building your first (and by default capitol) city. The most advantageous position for a city I have found is on a forest/jungle or hill tile with a river flowing through it. This adds the Production, Food and Defense bonuses automatically to your city. Building a city on top of a trade good is fine since it means your automatically work that good.
Never build a city on top of a swamp. When Global Warming occurs (almost inevitable) the swamp tile will be converted to water and the city will be destroyed.
One your city is founded start developing. Start with a list like this:
1). 3-4 Warriors.
2). A Granary-Food storage, prevents starvation and allows for faster population growth. Requires Domestication.
3). A Marketplace-+50% gold for that city.
4). 3 of your most powerful military units. Most likely these will be Phalanxes.
5). City Walls-+4 defence rating for units garrisoned within the city. Requires Stoneworking
6). A settler. I build a settler after every Wonder.
7). ASAP build the Labyrinth. Requires Shipbuilding.
Set your Public Works (PW) percentage to 20%.
You will know certain Advances. These are psedorandomly generated by the AI but most likely you'll know Domestication and Mining, maybe some others. Research Domestication if you don't know it, Bronzeworking, Shipbuilding and Stoneworking.
Once you have 2 warriors built, use one to explore. Fortify the other one as a city garrison until you can replace it with at least a Phalanx, preferably 2, or a Phalanx and an Archer/Mounted Archer. Warriors are more effective in reconnaisance than Mounted Archers because they can see 2 squares around them. Use them to find Ruins. Ruins are fundamental sometimes they will give you an Advance, military units or settlers, a new city or gold. Find them. Explore them.
Once all of this is established, start developing PW. Start with food production by placing Farms or Nets on every square you can within the 2-square site-radius around your city. Some sea squares will cost more to place nets on than normal (300PW vs. 200PW)-this means that there is a Undersea Trench underneath it, making placing a net there +50% more extensive in PW. Your citizens will automatically start working those squares and receive a Production boost. Placing the Nets there will result in a +5 Food boost. If you have a river flowing through Plains or Grassland near your city, place your Farms there. Improve all food-producing squares before placing Mines.
Once this is accomplished concentrate on building the Labyrinth and the Sphinx, exploring and founding cities to claim Trade Goods. Placing a city on an isthmus with fortified units within it is a good defensive strategy as is limits enemy movement through it. Where there is 1 land square separating 2 bodies of water, building a city there allows your ships to sail though, shortening their trip.
Once you have more than one city, start building Roads between them. Avoid building them over Swamps.