If, while trying to link your account to Google Play Games or Game Center, you are seeing a message that another account is already connected, it means that your current game progress is connected to the Google Play Games / Game Center account different from the one that is currently active on your mobile device.
To make it clearer, let's say your progress was connected to an xxxx@example.com account, and now another (yyyy@example.com) account is selected on the phone (or tablet). You get this error message only because a progress cannot be connected to two accounts at once. To connect progress to yyyy@example.com, first, in the "Accounts" / "Apple-ID" section of the general device settings, you need to log in to xxxx@example.com, return to the game and disconnect your progress from xxxx@example.com in the in-game settings.

If, when you are trying to connect your account to Google Play Games or Game Center, you are seeing an error message that you could not get a response from the server, please try again after a while.
 
In case of other types of devices and app stores, the steps are similar.