A clan allows players to unite under one coat of arms in a strategic alliance that would benefit all members. Clans enable users to develop rapidly and stay protected from enemy attacks, not to mention participation in specific tournaments is only available while one is part of a clan.
At the beginning of the game, you will be invited to join a computer-generated clan. Such clans don't have a leader or capital. They are designed to familiarize you with the basic clan mechanics and are very limited in the range of benefits they can offer compared to a player-created clan.
To join a player-created clan or create your own, you must leave the present clan first. Click "Leave clan" in the clan information tab.
Next, to create a clan, click the "Create a clan" button. You will be prompted to select your new clan name, a three-letter clan tag, and the emblem. Click "Create a clan" to confirm the operation, which will cost you 7.5K gold coins.  You can then select whether your clan should be private, request-only to join, or open for all to join, and select your clan's primary language.
To join a user-created clan, click the "Find a clan" button. You will be forwarded to your kingdom clan rankings, where you can browse clans and eventually join one or submit your application.