The copyright laws have a lot of provisions that are intended to enable use in education, teaching, research and scholarship. So the good news is that some instructional uses are 100% pre-approved allowable by law. Here are a few things you can do to use copyrightable materials in your teaching where copyright questions are easily resolved!
In-class Performance or Display
The "Classroom Use Exemption", allows performance or display of works in non-profit, face-to-face, in-person, classrooms or similar instructional settings. Playing a DVD or CD for a class (in whole or in part), singing a song together, or holding up purchased or borrowed copies of a book or artwork, would be permitted under this exemption.
Most courses at the University of Minnesota, if they meet in-person, are environments where the classroom use exemption will apply, and in-class performance or display is permitted by law without additional permissions. Teachers in many public and private non-profit instructional environments (K-12, or otherwise) may also make use of the Classroom Use Exemption. Instructors in other environments may wish to check with their administrations/legal counsel to see if the Classroom Use Exemption applies.
However, the Classroom Use Exemption does NOT cover making copies, or distributing them (whether the copies are for student use, or made as part of your preparations for class). It does not cover showing things in any other environment than an in-person one (not even simultaneous distance education technologies). It does not cover showing things in for-profit contexts, or in any context that is not class-based teaching. Some of the above situations may sometimes be allowed under fair use, or users may need permission.
Sharing Links with Students
Sharing a link with students via email, on paper, on a screen, or as a link within a course website or blog is almost always not a copyright issue. Linking to publicly available resources doesn't involve any of the rights covered by copyright (i.e., you're not making copies, or handing out copies, or creating derivative works...) so it's not usually a copyright issue!
Linking to subscription resources is also a great option for instructors - anyone who is supposed to have access as part of our institutional memberships will have access, and anyone who's not allowed to access via our subscriptions will be redirected. Meanwhile, since you, the instructor, haven't made or distributed any copies, you aren't raising any copyright issues. Creating links that work consistently can be a little challenging, but Libraries staff members are happy to assist UMN instructors, and we also provide step-by-step instructions if you want to do it yourself.
The one thing to be careful of when sharing links with students is linking to obviously infringing material - if you know (or should have noticed) that the stuff is not a legitimate copy, that can count as encouraging others to infringe copyrights. For example, you might want to avoid linking to an obviously-recorded-from-theater-seats YouTube copy of a movie that was just released in theaters last week.