There are many ways to play this game, but my preferred strategy is WAR.
During the first few turns, make 3 cities asap, and have one city churn out settlers, one churn out spearmen/warrior and one make workers. Then grab as much land as you can by making cities. And fortify at least 2 spearmen in each city.
When you have run out of space to expand, it's time for WAR! But first, assembly a decent sized army (you don't need a big army in the early ages), and then declare war on a civ near you. Then overrun the civ with your army and take their cities. If you need reinforcements anytime during the war, try to negoiate peace. If you have the upper hand, sometimes you can even get a city from them during the negoiations.
Then rinse and repeat until you're the sole dominant force in the game. Then you can decide what kind of victory you want.
That's why I usually play as Romans. They are the perfect civ for warring.