The entire map is divided into regions, each of which has several cities. Each captured city brings the clan a certain amount of Influence. If a city is lost, Influence is deducted. To fully capture the region of a clan you need to get more than 50% Influence in the region.
Participate in clan battles to earn Diplomacy Points for your clan, which the leader can then spend on a variety of strategic actions, such as attacking other cities and defending his own. But note, there is a limit to Diplomacy Points, after which they will no longer accumulate!
To capture a city you need to bring its HP to 0. After a capture, HP is fully restored.
In order to attack an enemy city, the head of the clan must select it and start the battle for Diplomacy Points.
When a clan attacks a city it goes into "under attack" status, and in this state no other clans can attack the city. The city remains under attack until a day goes by since the last hit, or until it is captured. In either of these cases, hp of the city is restored after it is no longer under attack.
If a city of a clan is attacked, the head of the clan can spend Diplomacy Points to restore it.