⇒ If the copyright holder's permission is needed, how do you get it?
If you couldn't answer YES to any question in Step 1, you'll need to seek the copyright holder's permission to include his/her work in your dissertation. Step 2 explains how to seek that permission.
⇒ Research & locate the copyright holder
In many cases, requesting permission to use published materials is straightforward. It’s best to start with the article or book publishers’ websites, which often have Web forms for making such requests. For example, here is IEEE's page spelling out how to make publication re-use requests.
In other cases, you might need to do some digging first to identify the copyright holder. Below are some suggestions if you need help. For more background, you may also wish to check out Peter Hirtle'sCopyright & Cultural Institutions, Chapter 8.
Materials from an Archive or Library Special Collections: It is possible (though not guaranteed) that the library or archive you used has donor information (if the donor was also the copyright holder), or transfer data that accompanied the acquisition of the collection.
WATCH File: The Writers, Artists, and Their Copyright Holders database contains primarily the names and addresses of copyright holders or contact persons for authors and artists whose archives are housed, in whole or in part, in libraries and archives in North America and the U.K.
Copyright Clearance Center: Commercial services like the Copyright Clearance Center can, for a fee, streamline the process by searching for the rights holder and securing the license for you.
⇒ Ask for permission in writing, and covering intended uses
Remember that your dissertation will be submitted to ProQuest and a copy will be available online in eScholarship - the UC system's online repository. So, when you contact the rights holder for a license, be sure that the rights you obtain cover online distribution. In addition, you may wish to request in advance worldwide rights for all formats if you intend to publish a subsequent book or articles using the same material; alternatively, you could go back to the rights holder later and ask for permission for these subsequent publications.
Be sure to ask for permission in writing and keep records for your files, just as you did with a fair use analysis. This will be important not just if the copyright holder later challenges your use, but also if your later publisher asks to see these conveyances of permission. Written requests (even if unanswered) can at times also be considered evidence of good faith should your use be challenged.
Here are some useful sample permission request letters:
The University of Michigan also has an excellent guide on securing permissions for copyrighted resources--including for films, book chapters, music, fine art, photos, and more.
Keep in mind that, even if you believe your use would be fair regardless of whether you're subsequently publishing commercially, your publisher may require you to secure permissions merely as a matter of policy. Ultimately, you'll have to make a judgment call about whether, in anticipation of future book publishing needs, you choose to ask copyright holders now for their permission to publish both in your dissertation and all subsequent commercial endeavors.
⇒ Silence is not permission
If you do not hear back in response to your request, this does not mean you automatically have rights to publish the material; a copyright holder can still later challenge your use. A copyright holder's silence turns the situation into one of risk assessment for you--you'll have to consider whether to keep seeking permission, the likelihood (or not) of the rights holder challenging your use, and (possibly) whether to use different material or leave it out.
⇒ Plan ahead
It can take weeks (or months) to hear back from rights holders. And, remember you need to go through this permission process for each copyrighted work that you're using beyond fair use. So, it's best to get started early with permissions-seeking in the research and writing process.