Note: The only reason you would currently have to do this is if you previously purchased something under a different account and need to restore it following a major event (such as reinstalling the game).
On an iOS device:
On an Android device running Google Play:
On a Kindle Fire:
The instructions on this page for deregistering and registering an email address should help you with this process. Note that it is an Amazon webpage, not a Spry Fox webpage.