You can create or join a clan from the Clan window, which you can open from the menu by clicking the shield icon. Creating a clan is not free but if they can do it so can you. Alternatively you can join an existing clan providing you find one that you like.
Depending on your rank in a clan you may have access to the clan vault, which is similar to your personal bank, but is accessible to those that have a sufficient rank to use it. The clan leader (SupremeGeneral) can set the required ranks along with other various clan related settings.
Leaving a clan is a long transaction as it takes 45 minutes to fully leave the clan.