First, select the "Clans" tab. You'll be shown a list of Clans that are available to join! Just tap the "join" button on any clan you'd like. However, some Clans have their permissions set so that you have to request to join, but don't fret! Just hit the "request" button for the Clan leader's approval!

 

Congratulations, you've joined a clan! Now go and complete some missions!