All your work is saved automatically in The Land App. There is no save button.
To be certain that everything has saved a timestamp is visible just below the name of your map in the top-left corner of the screen.
If your internet connection fails and you continue to edit in the map, you will automatically be notified that your map is not currently being saved:
Once your internet connection is restored, the map will return to saving automatically, which you can confirm by viewing the timestamp.