Currently the only method of account backup or transfer is through Line. Once you have an account you like and you are sure you will be keeping it, go to the App marketplace for your device (Play Store or App Store) and download the Line application.
Login or create an account on the Line app. Go to your game, click the settings cog in the top right hand corner and click the button with the icon shown below:
It will then prompt you to allow the game to have access to your Line account, after allowing this you should be all backed up. To test if it has worked see if the icon above is still in your menu (you may have to reset the game for it to disappear) if it is still there then your account is not linked but if it is there then you are set!
In order to transfer to a new device, on the new device download the game and play through the tutorial, as above click on the icon shown and login to line, you will be prompted with the message below, click on the button to the left and accept that you want to recover account from line, at this point it should kick you back to the startup screen but once you reload the game you should be back in your saved account