The automatic backup uses Android's built-in mechanism for saving and restoring user data, which requires Google Play Services to be enabled and storage from Google Cloud. This solution is the easiest and safest to use, as changes are tracked in the background and user data is automatically restored when you buy a new device and reinstall the Fakebook app. In theory, at least...
Unfortunately, not all devices has Google Play Services and the necessary transport and storage to the cloud, which makes Android automatic backup less than ideal.
This is why Fakebook also comes with a simple to use manual backup. Just go to Database and backup in the Settings menu, then select Perform manual backup. After a few seconds (depending on the size of the database) you will be prompted to send the backup file to Dropbox, Drive, a mail or similar. Now keep this file safe until yo need it.
Should you need to restore the backup, e.g. on a new device, again go to Database and backup in the Settings menu. This time select Restore manual backup. A file dialog opens to let you chose the backup file. Select it and wait until the database is installed. Note that the backup will completely overwrite any existing database, e.g. the pre-installed songs.