From the home screen, there should be a button that says "clear cache". This will not delete your data, instead it will clear a lot of unnecessary space that the app takes up so you may have enough for your other app. In the end you have to redownload all of the data so...
But to actually backup your account, you must click on this
And either connect your google account OR make a password. I think its more efficient to make a password imo. If you choose to make a password, the game will then give you a transfer ID and the password you wrote down. Make sure you have written down the ID and password, or take a screenshot of it.