Check the pages--straighten the corners of the pages that are bent. This will take some time but it will be worth it.
Place the book under some heavy books or weights overnight. How long it will take to flatten the book will depend on how badly the book is bent.
Use care in handling your paperback books. When reading your paperback book, use extreme care so the book doesn't get bent. Use a bookmark instead of bending the pages.
Protect the covers of your paperback book by covering them. This doesn't have to be anything fancy. You can use paper bags or you can get book covers. If you buy book covers, you can use them repeatedly for each paperback book while you are reading it.
Put your paperback books on a shelf between two other heavy weight books to flatten it. This will take longer to accomplish your goal, but it will do the trick.
Store your paperback books on shelves--if you fit them in nice and tight this will keep them flat.