If a city has walls built the only way to conquer it is to mount a siege. To mount a siege an army must be moved to the location of the city. Then the siege timer must expire before the army sieging the city will lunch an attack. The siege timer duration depends on the difference in the number of cities the attacker and the defender own. The bigger the difference in favor of the attacker the more time the siege will last giving the defender more time to prepare.
Once the siege time has expired the army will attack the city. Before the attackers army can engage the defenders the walls must be destroyed, which can be accomplished with Catapult or Trebuchet units. The attackers artillery will fire each round until the walls are down. If the 15th round is reached with the walls still standing the battle will end in a draw. Until the walls are down the defenders ranged units will have free reign to fire on the attackers without retaliation from the attacker ranged units. If the attacker is successfull in bringing down the walls a standard ground battle will ensue.
Assuming the attacker has won the battle the city will be either conquered or destroyed, it dependes on the amount of cities of the attacker and defender. If the attacker has an equal amount or less of cities than the defender then the city will be conquered, else it will be destroyed.