The more excess food your city produces the faster it grows. Put your citizens to work on bonus grassland, squares with wheat and cows, irrigated plains. Once youre' in Monarchy or Republic, irrigate grassland for more food. Flood plains give you lots of food especially when irrigated. Build a granary and the city only needs half as much food to expand.
Build cities: 1-Next to fresh water (then they don't need Aqueducts to grow past size 6), 2-near luxury and strategic resources, 3-near hills/mountains with gold deposits, 4-near food bonus tiles, 5-in places that make it hard for the AI to expand.
Check Bamspeedy's "Deity Settlers" in the War Academy in addition to the "Opening Moves" article that superlon linked.