If you are not in a clan, you will see two options in the bottom-right corner of the screen when you are on the Clan or Clan Chat tabs. These options are "Create" and "Join". If you tap the "Join" option, you will be shown a list of recommended clans with some stats on the right. From left to right, these icons are Recruitment Type, Number of Players, and Trophies.
The Recruitment type will either show no icon or an envelope for each clan. If the clan has an envelope in this column, this indicates that the clan is set to "Invite Only" and you will need to request to join. This can be done by tapping the clan, and tapping the "Request To Join" button at the top. Once the leader of the clan you requested to join looks at their clan chat, they will see your request and can either accept or reject it. If they choose "Accept", you will get a message in your inbox noting that the clan has accepted your request to join their clan. Then simply tap "Accept" to join, or "Reject" if you have decided against joining this clan.
If there is no icon in this column, this indicates that the clan is set to "Open" and anyone can join at any time provided there is space. This can be done by tapping the clan, and tapping the "Join" button at the top.
The Number of Players stat will show a value between 1 to 50. Note that a clan can hold up to 50 players at one time.
The Trophy stat indicates the total number of trophies that the clan has earned. This value increases when players win PvP matches when in the clan.
You can also find clans to join on the Recruit tab. If you see a message that says "Looking for new members." you can tap the "View Clan" button to the right, and then join in the same way as mentioned before.