Bookbinding is almost a lost art. Learning bookbinding skills is a great hobby, plus it allows you to have personalized bindings on your favorite books. One of these important skills is how to remove the original binding without damaging your books.
Survey the book and consider the type of binding you are working with.
Purchase a set of bookbinding tools, such as those found on Peachey's website, to remove a traditional binding. Use these tools, particularly the scalpel, to help remove the book's binding without damaging the pages.
Eliminate the hard cover of the book quickly. Open it up, and cut along both interior folds using a sharp scalpel or utility knife. Use caution and score in a direction that will not cut you.
Pull the spine away from the book cover, gently, after removing the hard cover. View the glue and binding threads on the spine area. Pull one of the threads to see if you can get the binding to separate from the spine. Continue to peel off threads until you remove all of the binding.
Note that there is still quite a bit of glue holding the pages together. This is what saves you from damaging the pages as you rebind the book.
Note
If you have a plastic spiral type binding, this is definitely non-damaging. Simply slide out the spines to remove the binding.