Citizens become unhappy (All of the new ones) after you have a population of 5 on chieftan, 4 on warlord, 3 on regent, and 2 on monarch+, IIRC.
Temples will make a person become content in the city they atre built in, the Oracle makes temples more effective.
Colliseums make 3 people content and cathedrals 4.
Another way to create happiness, as has been mentioned, is by making an entertainer, but you lose food and production for it.
Basically, if you are having overpopulation problems early in the game you are expanding way too slowly, particularly when you are at the lower levels.
I usually build a scout, a warrior, and start cranking out settlers as fast as I can with occasional military units in between.
Communist gets up to 4 units/city where a unit makes people content, monarchy and despotism 2.
Man, after playing a more militaristic game, I am really liking communism, I would highly reccomend you use it if you plan on steamrolling over your foes.