you're supposed to build more cities over time (you do that by building a settler then moving him to a nearby square) but you're constrained by the fact that building a new city often makes your happiness go down. and when your happiness is too low you get various penalties so you have to manage that. I think new city happiness is something like -4 but it's been a while. if you're somewhere above that it should be okay to expand.
also worth mentioning is that you have a meter that slowly builds when you have positive happiness. if your empire is 20 happy you get 20 points per round etc. get to the next meter goal and you get a golden age which gives your civ all kinds of bonuses. so it's good to keep your civ extra happy. but you also gotta expand, because most victory conditions at least are more likely when you have a few cities.
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http://www.youtube.com/watch?v=npHDxSvwCE0