If copyright gave creators the ability to completely control all uses of their works, creativity and culture would soon grind to a halt. No work is created in a vacuum; all new works build on, are influenced by, and make reference to works that have gone before. Moreover, since copyright has some fundamental public interest purposes, it's important that the public be able to do some kinds of things with all works.
Copyright law places a high value on educational uses. The Classroom Use Exemption (17 U.S.C. §110(1)) only applies in very limited situations, but where it does apply, it gives some pretty clear rights.
To qualify for this exemption, you must: be in a classroom ("or similar place devoted to instruction"). Be there in person, engaged in face-to-face teaching activities. Be at a nonprofit educational institution. Sounds a little restrictive?
If (and only if!) you meet these conditions, the exemption gives both instructors and students broad rights to perform or display any works. That means instructors can play movies and music for their students, at any length (though not from illegitimate copies!). Instructors can show students images, or original artworks. Students can perform arias, read poems, and act out scenes. And students and instructors can do all these things without seeking permission, without giving anyone payment, and without having to deal with the complications of fair use.
The Classroom Use Exemption does not apply outside the nonprofit, in-person, classroom teaching environment! It doesn't apply online - even to wholly course-related activities and course websites. It doesn't apply to interactions that are not in-person - even simultaneous distance learning interactions. It doesn't apply at for-profit educational institutions.
The Classroom Use Exemption also only authorizes performance or display. If you are making or distributing copies (i.e., handing out readings in class), that is not an activity that the Classroom Use Exemption applies to.
The TEACH Act (17 U.S.C. §110(2)) does create some rights for teaching uses of copyrightable works in the online environment, but it's much more technical and there are a lot more restrictions.
Fair use (17 U.S.C. §107) is a BIG limitation on the rights of copyright owners. Because of fair use, certain kinds of uses are allowed, without permission or payment - in fact, even in the face of an explicit denial of permission - at any point during the copyright term. Fair use is why things like quoting a book in order to review it, or publicly displaying a reproduction of an artwork in order to critique it, are legal.
First sale (17 U.S.C. §109) limits a copyright owner's right to control distribution of copies - once a single copy has been sold, that particular copy can be redistributed, by anyone, through resale, lending or donation. First sale is one of the legal rules through which libraries are able to lend materials in their collections to their user communities. It's also how the used book, CD, movie, game, and software markets work, although End-User License Agreements are beginning to have serious restrictive effects.
There are lots of other exceptions, exemptions, and limitations in copyright. A few interesting examples: