To join a Clan, you need to be at least level 25. If you want to join a clan, tap the Clan icon in the bottom right corner of the game screen, then the Join tab.
Here you can either scroll through the list of clans or search for a particular one by name. After you find a clan you like, tap Open and then Join.
NOTE: Along with other requirements, a clan can have open admission or accept players only by invitation.