FSU Libraries' Copyright FAQ includes a wealth of helpful information about copyright concerns related to theses and dissertations.
You should assume that anything produced by someone other than yourself is protected by copyright unless you determine otherwise (e.g. determine that the term of copyright protection has expired and the work is in the public domain). The types of works protected by copyright include books, articles, newspapers, photographs, music, movies, software, and even things you find on the internet.
Use of works protected by copyright in your dissertation or thesis will need either permission or a fair use justification. Fair use is an exception to the copyright holder's exclusive rights. In order to use copyrighted works under a claim of fair use, the following factors must be weighed: (1) the purpose and character of the use, including whether such use is of a commercial nature or is for non-profit educational purposes; (2) the nature of the copyrighted work; (3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and (4) the effect of the use upon the potential market for or value of the copyrighted work. For more on fair use, click on the Fair Use tab in the sidebar.
Fair use provides an indispensable opportunity for scholarship, since so much of research involves building upon the insights of others. Quotations from other writers are a regular part of most scholarship and are generally consider a classic example of fair use. There is no exact rule about how much one may quote and remain within the boundaries of fair use. Various guidelines that offer specific numbers of words or lines are advisory and do not have the force of law. In general, quotations from the work of others should be no longer than is necessary to support the scholarly point you wish to make. When you are subjecting the quoted material to scholarly criticism or comment, you have more leeway for fair use than in many other situations, but you should be sure that you do not use more of someone else's work than is necessary for the argument that you are making in your own thesis/dissertation.
In the case of images, you should be sure that the pictures you reproduce are closely tied to your research goals and are each made the subject of specific scholarly comment. If you use a large number of copyright-protected images by a single artist, or in some other way threaten to supersede the market for the original works, it is wise to seek permission. If you have flexibility in the final selection of your images, search for images that are 1) in the public domain, or 2) made available for reuse via a Creative Commons license. Such images can be incorporated into your dissertation without permission or concern for fair use.
If you determine that permission is necessary, the first step is to locate the copyright holder. This may not always be the author; sometimes copyright ownership is transferred to a publisher or to an author's estate if he or she is deceased. The Scholarly Communications Librarian can assist you with determining who is the owner of copyright. Once you determine who to request permission from, it is best to send a written letter of request. An email letter is sufficient. Model permissions letters can be viewed here. It is best to get written documentation of permissions. You should retain copies of all permissions in your files.
Finally, remember to always provide proper attribution to the sources of the works you incorporate into your thesis or dissertation. Proper attribution is absolutely required; that’s a part of academic integrity and good scholarship. Copyright permission, if necessary, is an entirely separate matter and does not obviate the need for attribution.
Columbia University Advisory Office - "Permissions"
ProQuest/Kenny Crews - "Copyright and Your Dissertation or Thesis: Ownership, Fair Use, and Your Rights and Responsibilities"
University of Michigan - "A Graduate Student's Guide to Copyright: Open Access, Fair Use, and Permissions"