New to Civilization

Hello I got Civilization 4 all the way to brave new world for Christmas. I am laying as Rome, on the settler level, on standard speed. I have yet to win a game because I have not figured out how to take over a country, or city state. There is this one city state, I have depleted the green health bar many times and I but it is still there, I have expanded my empire to the point that there is not neutral land between me and the city states, or Babylon. but I can not seem to take anything. What am I doing wrong?

Moderator Action: Moved to Civ V - General Discussions.

You can only take a city with a non-ranged unit, such as a warrior, spearman, horseman, etc. All your ranged units can do is knock down the city's HP enough to allow your melee units to take the city.

You have to use a melee unit, such as a warrior, swordsman, or pikeman. You have to have them attack the city when its health is very low to capture it. You have to enter the city, instead of just bombarding it.

Man I remember when I had just gotten the game I did that exact thing! I kept thinking why won't this city fall! But yes you need to walk a Melee unit in