1. Do you need permission?
Is what you are using protected by copyright? Aren't sure? For a list of what types of work that are typically considered protected by copyright, check the What is copyrighted list here.
You should not need permission if any one of the following is true:
2. Get permission from the copyright holder
If your work isn't in the public domain, or licensed to share, or fair use isn't applicable, then most likely you will need to seek permission to use the material. But how do you do that?
First, keep in mind that getting permission can take a while so you should plan ahead.
3. Decide how to manage your copyright
What about registering your copyright?
Your thesis or dissertation is automatically copyrighted once it is in a fixed, tangible medium. That is once your work is recorded, whether in print or in a computer file.
You don't need to register for copyright because copyright is implicit. Once your work is finalized, it is considered copyrighted. In some cases, you might want to further protect your work by registering it with the U.S. Copyright Office. Such formal registration provides very strong protection of your rights against infringers or plagiarists because registration is a public record that you are the owner and author. For an in-depth discussion of this topic, see Dr. Kenneth Crews Copyright and Your Dissertation or Thesis: Ownership, Fair Use, and Your Rights and Responsibilities.
What about putting an embargo on your thesis/dissertation?
There are some instances where you might want to consider requesting that your work be embargoed for up to two years. Here are a few examples: your work contains patentable rights, or you have ethical concerns, or your journal/book publisher has requested it. You should consult with your advisor about whether to request an embargo or not. Forms for master theses embargos are here and for dissertations are here.
What about licensing your thesis or dissertation beyond fair use?
Other scholars can use your copyright work for their research within the framework of fair use. But you can license your work beyond what is allowable under fair use with a Creative Commons license. These licenses are focused on broader access, varying in what usage is allowed, although these licenses are much more flexible than copyright law. If interested, explore these options with your advisor.