Section 110 of the copyright law allows for clips, complete videos, and music to be studied in the classroom setting. Generally, then, in face to face teaching you are protected by an exemption in the copyright law. However, there are a few underlying requirements to this exemption.
The other issue is if your copy is an off-air recording. Stanford provides a useful overview of the requirements. The quick restriction is that the recording needs to be from a broadcast channel (not HBO for example) and it can only be shown to your class within 10 days of recording the program. Again, look at the Stanford page for more guidance.
Copying depends on the nature of what is being copied and the amount copied.
Single copies: Generally, any single copy to use for research or teaching is going to be protected by fair use.
Mulitple copies: You want to apply a fair use analysis for any work you choose. Some suggest the classroom guidelines of 1976 are a "safe-harbor." As a minimum:
These guidelines were never codified as part of the law and represent minimums. They have also been criticized since their inception, particularly the one course, one term and 10% minimum. The best approach would be to make a fair use examination of the material.
One final note - A clear area is the consideration that copying should not replace book purchases. In particular, consumables, such as workbooks designed for the education market should not be copied.