Research the publication information. If the work is out of copyright or published before 1900, it should be in the common domain. You wouldn't have to secure any official rights.
Contact the publisher and the author. Depending on the contract between the two, the rights to movie adaptation rest with one or the other. Negotiating the movie rights can take a few months, but you should be able to secure an option to adapt the work. The option should specify how much you will pay if you go ahead and buy the rights. While you have the option you put together the production and funding. The typical contract for the rights is for five years; if you haven't made the movie by then the rights might revert back to the publisher or author.
Call any producers that have already bought the movie rights. Perhaps the project has fallen through, and the producer is willing to sell the rights off.
Sign the contract, and promptly pay for the rights. All documents should be vetted by your attorney to make sure that you and your creative work is protected.