To exit from the book, tap at top left until the <Kindle bar appears, then tap the left arrow before the word "Kindle".
To delete a book, press and hold on that book in the list until the popup window appears then choose "Remove from Device" - that will move it to the "archive" and out of the list of "active" books.
To examine or work with the Archive, click the down arrow to the right of the line that says "Library > DownLoaded Items | v" or "Library > All Items (20) | v" etc and choose "Archived Items" from the drop down list, etc.