The Guidelines for off-air recording of television broadcast programming for educational purposes state:
These rules of thumb are based on the 1979 "Guidelines for Off-Air Recording of Broadcast Programming for Educational Purposes," contained in the House Report on Piracy and Counterfeiting Amendments (H.R. No. 495, 97th Cong., 1st Sess. at 8-9), as well as the Supreme Court decision in Sony Corp. of America v. Universal City Studios, 464 U.S. 417 (1984).
There is no rule that allows use of even a small amount of a video clip of a television program outside of the classroom guidelines. without permission from the copyright holder. Unless an exception to copyright applies, you need to obtain permission from the copyright holder.
If the library has a purchased copy of a television program (generally video or DVD) in its collection and you want to put it on reserve in the library for a specific class, contact the Library. See Libguide tab on copyright of DVDs or videos. If there is any question, library staff will check at the source to determine needed copyright permission.
You are responsible for copyright permission for your own web site. Is your web site in a secure location where only your students will be able to view the programming?
Just because something is on the Internet and is easy to use, does not mean it is free to use! Be sure to cite or attribute what you do use appropriately. Internet resources often combine both copyrighted and public domain content. Use care in downloading any content from websites. Check site to see if permission should be requested or if allowed.
Be aware of the copyright ramifications of including embedded additional links to that particular site. Deep linking to pages several levels deep within a site may also lose this context and raise the objections of a site owner. These are at the very least courtesy situations and may be considered contributory infringement. In losing context, you may obscure attribution.