Once you reach level 5 and unlock the white Beach Club cabana, you can create your own Beach Club.
To create a Beach Club, tap the white cabana and go to the Browse Clubs tab and tap the Create button in the top bar.
Fill in the Beach Club name and motto, choose the approval setting, select a Beach Club flag, and choose a level requirement (players must be that level or higher to join).
When you're happy with your choices, tap the green Create button at the bottom to start your own Beach Club!
Note: The starting level requirement is level 5 because players need to unlock access to Beach Clubs in order to join any Club, however you can raise the minimum level for the players you want to allow into your Beach Club.
The maximum level requirement is based upon your own level.