From my observations playing as dwarf:
You get more charter as you research.
Early game you get 3 charter which is enough as a size 1 city costs your economy a lot of gold to maintain so it will take a while before you could afford a fourth city.
I went to war with another civ and demanded one of their cities in exchange for peace, when they were down to one defender they gave me a city.
After a while i took their Capital by force.
Two civs that had been beaten down to their last city traded me their charter so i built new cities and went on a science binge that gave me a further 2 or 3 charter.