First, you need to deregister the Kindle from the old account.
Deregistering will retain the already downloaded books on the E-Ink devices but wipes all purchased content tied to the old account from e.g. Kindle Fire. You cannot restore books from the cloud anymore you purchased on the old account and access to the shop is blocked until the device is registered again. Other Kindle's on the same account and the account itself remain unaffected.
You can do the deregistration from the Kindle's settings menu --> Registration or alternatively from an Amazon web site:
Log in to
http://kindle.amazon.com using the old credentials (email + password).
Next, select "Manage Your Kindle" from menu that opens when you hover the mouse over the "Hello, <Name>" link in the upper right corner of the page.
Click on the center tab "Your Devices" and review the list of Kindle devices and software readers tied to your account. Select the device to deregister and click on "deregister" below.
To register the Kindle to a new account, go online with the Kindle, and follow the registration procedure callable from the settings menu. Find a detailed description on
http://www.amazon.com/gp/help/customer/display.html?nodeId=201242220
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