In order to create your own League you must be at least Level 30 and it will cost you 1000 Sapphire. The other option is to join an existing League, which you can do by going to your embassy. To join, your request needs to be accepted by the League leader and you must be at least Level 16.
Note: Your League's position within the League Rankings and influence on the game map will be determined by the total output of the Beacons currently controlled by your League.
Thanks for reading and feel free to comment with any comments, questions or concerns you may have about Leagues and/or Beacons!