In order to expand your realm you must build new cities. It's also possible to conquer new cities, however it's a difficult task at the beggining and takes time.
In order to build a city an army must have the following amount of resources:
The gold cost varies depending on the number of cities you control:
(number of cities)1.25 x 1000
Once the army has enough resources it must be placed on a tile suitable to build a city. You can control if a tile is able to host a city by clicking on the desired tile. You can also calculate the resources and attributes the city will have if put on that spot by clicking the "Calculate city resources" link.
Finally, once the army is on the right tile just click the "Build a City" link.
Conquering a city is only possible if the defender controls a number less or equal of cities than the attacker. If that's no the case the city will be destroyed instead of conquered.
In order to conquer a city the attacker must first siege the city (if the city has Walls). The battle for the city will start once the siege timer is over. The duration of the siege timer is influenced by the level of the Walls (the bigger the Walls, more time is added to the siege timer) and by the number of cities the attacker and the defender have. If the attacker has more cities than the defender then the siege will take more time.