You can do this by connecting to Supercell ID, Apple ID, or Facebook Login in the game settings. Tap on the cogwheel in the top right corner of the Mansion screen to access these features. 
 
Connecting to Supercell ID, Apple ID, or Facebook Login means that your game progress will be saved to the cloud.
 
If you wish to move to or use another device:
 
1. Connect to Supercell ID, Apple ID, or Facebook Login on your existing device.
2. Install Merge Mansion on the new device.
3. Sign in to Supercell ID, Apple ID, or Facebook Login - whichever you previously chose - on the new device. 
4. Your progress is now available on both devices.
 
Please note that Apple ID is only available on iOS devices with iOS 13 or newer. If you are changing platforms from Apple to Google or vice versa, either Supercell ID or Facebook Login can be used.
 
We highly recommend you connect to save your progress. If you don’t want to connect your game and you are changing phones or planning on resetting your device, you can ask Support to transfer your game progress over to the new device by contacting us from within Merge Mansion.
 
To initiate the transfer, simply get in touch with us through the "Settings" menu. The Player ID is attached to the messages you send to Support, so the easiest way to provide it is simply sending a message from both the old and new device, asking for a transfer.