To delete a book from a touch screen Kindle, scroll through the list of titles, then hold down on the book you want to delete. Select "Remove from Device" when the menu pops up. For non-touch screen Kindles, go to the home screen, then select the title you wish to delete. Press the right direction button on the five-way controller to display an action list, and select "Remove from Device" using the center button.
Deleting the book from the physical Kindle device does not delete it from the Amazon Cloud. It can be downloaded again at a later date unless it is permanently deleted from Amazon.com.
To permanently delete a book, log on to Amazon, click on "Your Account" and scroll down the menu that pops up to "Manage Your Content and Devices." Under the "Your Content" tab, select the title you wish to delete, and click on the "Delete from Library" option. Amazon will ask you to confirm that you want to permanently delete the item from your account. Once an item has been permanently deleted from the website, it is gone forever, and Amazon requires that it be purchased and downloaded again if you want to access it.