To backup your progress in Legend of Solgard, you need to make sure your game is connected to Google Play.
To connect to Google Play, follow these instructions:
Open the Google Play Store on your phone
Search for and install “Google Play Games” on your device
Open Google Play Games app and create an account or login if you already have one
Open Legends of Solgard app
Tap on the Settings icon in top left corner
Tap on ‘Connect’ (green button)
The app will automatically try to connect to Google Play Games with your logged in account