If you do not have a Facebook account, or if you do not want to use it to save your game, you can use one of the following services instead.

Apple
Log into Apple Game Center. To do so, register a new account, or use your existing one if you already have one.
Press here to create a new Apple ID.
To access your account with your Apple ID (usually it matches your email address), press here.
If you have previously made purchases via iTunes Store and App Store, or have a Game Center account, you can use the same Apple ID you used with these services.

Android
Google Play Games service. To do so, register a new account, or use your existing one if you already have one.
Press here to create a Google account.
Press here to log into an existing Google account.

Keep in mind that without a Facebook connection, you will not be able to move your game from one device to another even if their operating systems differ. You will also be limited in your choice of what device you can play the game from. You can find out more about the benefits of linking your game to your Facebook account in the relevant FAQ section.

Have fun playing the game!