Curl the cover of the paperback book inward, very gently, in the opposite direction of the existing curl, then carefully uncurl it again.
Place the closed paperback on a flat, solid surface.
Put the heaviest hardcover book you have on top of the paperback. The hardcover ideally should be larger than the paperback. If needed, add an extra weight on top of the hardcover book.
Leave the hardcover book in place overnight, or for 10 to 12 hours.
Remove the hardcover book and the paperback book's cover should now be flat. If a slight curl still remains, put the hardcover book back on top and leave it for another 10 to 12 hours.