To save your progress and current base, you should Bind it to Game Center (More options will be available in the future)
To do so, on the main command interface, tap the More button in the lower left area. After which, select Account from the available options.
Select Game Center from the menu. You should be logged on to the service in order for this to work. You can bind only one account to Game Center.
Once done, your progress will be saved under the specified credentials. If you wish to make any changes on that, you can contact our customer support and they will help you out with any requests you may have.