To mention a theory and talk about how it relates to your project, you do not need to obtain permissions-- unless you are using a figure, diagram, or image in your published work. To use a concrete representation of the theory, you will need to obtain permission from the actual creator of the figure, diagram, or image.
There are always exceptions, so don't be afraid to reach out to the library or your professor with any questions. Additionally, it's never a bad idea to make a scholarly connection and reach out to any living theorists to let them know you are using their theory.
You will need to get permission to reprint or adapt any material that is currently under copyright. While some authors or publishers may not require permission for use of their material in a scholarly work, this is something that you will need to consider carefully. Not seeking permission can have an impact on your ability to publish your work. It is in your best interest to seek permission for copyrighted material early in your research and writing process; it may take longer than you anticipate to receive permission if you need to contact an author or content creator directly.
If the material you want to use is licensed under Creative Commons or if it's in the public domain, you do not need to request permission. You will still need to include a copyright attribution, but you do not need to seek permission before using the work. The only exception to this is if the work is under a NoDerivs Creative Commons license (e.g., CC BY-ND 4.0) and you wish to adapt the material. You will need to seek out the content creator and get permission before making any adaptations.
Not necessarily! You should always cite your sources to indicate the source of information and ideas in your research. Attribution (or citation), however, is separate from permission. The copyright holder has exclusive rights to reproducing the work. Keep in mind, the author of the work may not be the copyright holder. For example, when an author publishes a book or a journal article, copyright often falls into the hands of the publisher.
From Attribution is Different than Copyright Permission, by the Copyright Clearance Center, 2016 (http://www.copyright.com/learn/media-download/attribution-different-copyright-permission/).
The short answer is find the copyright holder and ask.
The key thing is to identify who holds the copyright to the work you'd like to reprint or adapt. For example, if you're looking at a figure from a journal article, the copyright may remain with the author(s) or it may be registered under the publisher. In order to identify who holds the copyright to the material you'd like to use, try revisiting the DOI or URL associated with the article or work. Many journals or publishers will include a link or statement about "Rights and Permissions" or "Reprints" or something along those lines.
If you've found an image online and there is no attribution or the owner is unclear, you can use a reverse image search engine to identify the important details you need to know. A reverse image search can tell you where the image came from, where it's being used and if there's a high-resolution version. TinEye and Google Images both have instructions about how to do a reverse image search using their respective platforms.
It's best to get permission in writing, whether by sending a letter and including a self-addressed stamped envelope or through e-mail or through a third-party copyright administrator (e.g., the Copyright Clearance Center). You want to have documentation for your records.
It depends on who holds the copyright for the work in question. Sometimes you will need to contact the publisher of the journal or book. Many publishers work with the Copyright Clearance Center to administer rights and permissions; other publishers require you to contact them individually. Check with the Copyright Clearance Center first to see if they handle permissions requests for your source.
There are other situations where you may need to contact the author or creator of the work directly. In this case, make sure to review the article carefully since a "corresponding author" may be listed that will represent the larger group of authors in any communications or inquiries.
Great! If you're reprinting or adapting a table or figure, make sure to include that you've received permission to do so in the table or figure note.
You should also include a copy of the permission in your appendices. This might be a letter or e-mail or some other document.