I fully agree with the answer from @DavidSiegel but provide some additional comments.
how do you formally record that you were given permission and the
precise terms of agreement of what you may and may not do in your
derivative work? Is there a classic contract format for this?
While an actual transfer of copyright ownership must be made a matter of public record, a contract granting permission to make a derivative work from a copyrighted work, called a license, does not have to be and typically is not a matter of public record. It is normally memorialized in a written contract signed by the copyright owner and a representative of the licensee.
While short licensing agreements of a page or two aren't uncommon in some contexts, an agreement to license of video production of a novel, for example, would often be an extremely lengthy and detailed contract running to ten to eighty pages.
For example, I have a textbook on intellectual property licensing in my office that runs to about eight hundred and thirty pages, about two-thirds of which consists of form licensing agreements or parts of licensing agreements, addressing a variety of different subjects, and the vast majority of which are quite lengthy. But there are no official government safe harbor forms for licensing agreements. Also, the subfield of law dealing with licensing agreements is insular enough that there aren't even many widely available commercial forms for handling that kind of transaction.
The primary licensing arrangement to produce the videos for the video production itself may not necessarily be all that complicated on its own, but the licensing arrangement will also have lots of sections related to spin off merchandise, rebroadcast and streaming rights, reissues of the original work with images from the new production, confidentiality to maintain message discipline in the marketing of the new video works, dispute resolution procedures, international licensing rights, an option to extend the license to a sequel, etc.
If you'd like to find some examples, there are probably some in the Security and Exchange Commission's EDGAR database of securities disclosures made by publicly held corporations because publicly held corporations subject to U.S. securities laws (including all companies trade on U.S. stock exchanges) are required to disclose the material provision of their key contracts to the general public via filings with the SEC, and some of them have probably entered into that kind of licensing agreement.
Still, licensing agreements are not by a long shot the most involved contracts typically involved in doing a video adaptation of a novel. Hollywood contracts regarding the financing of these productions and the way that profits are shared are much more involved.
As a practical matter, most video adaptations of existing works are financed in part by making the owner of the original work an executive producer of the video version who receives a large part of the total compensation that the copyright owner receives in the licensing deal in the form of shared profits from the production. So, in addition to the licensing agreement itself, the copyright owner will also be a party to the arcane agreement (basically, very complicated limited liability company or limited partnership operating agreements) setting forth the profit and loss sharing waterfall for the production which will have percentages for the director, star actors, copyright owner, producers, soundtrack composer, and some other top tier players in the production. These agreements often use different formulas for different possible outcomes and have different percentages for different sources of potential future revenue for the production and its related spinoffs and future distribution.