In order to delete a book from the Class Shelf that a student added, you or the student need to delete all of the work associated with that book.
From a teacher account (Silver and Gold only):
Go to Data, and click on the student who added the book. From the Books table for that student, click the View link next to any work listed to the right of that book:
On the next page, click on Edit underneath the quiz score, and then click on the Delete link to delete that piece of work. Do this with all the work listed on the text table for the book you want to be removed. Once there is no work for that book, it will no longer be listed on the Class Shelf.
From a student account (only if enabled by the teacher in Settings):
Go to My Shelf and click on the book. Click the tabs at the top to go through and delete all work under that book using the Options drop-down:
Note: For Silver and Gold plans, you will also need to delete any reading logged for that book. See Edit Logged Reading.