For DL Reader on iOS devices, go to the bookshelf (or library).
If the bookshelf shows the books in a list view, swipe from right to left. The delete option will show.
If the bookshelf shows the books in thumbnail view, tap and hold the book's thumbnail. An "x" will appear at the top left corner of the book. Tap the "x." Two fields pop up at the bottom of the app. You can select "Delete Book" to delete the book from the app or "Cancel" to return to the bookshelf.
For DL Reader on Android devices, tap and hold the book. A text field appears naming the book you selected along with two options. The first says, "See book details" to see book information. The second says, "Delete permanently" or "Remove from device" (depending on type of book/loan).