Most images and video produced in the United States protected by copyright law, and cannot be re-used without the permission of the copyright holder (often the creator). There are three categories of material that you can use in spite of copyright law.
Public Domain Material
Material whose copyright has expired and works produced by the federal government. This material can be used by anyone for any purpose. Consult Peter Hirtle's copyright term chart to see if a work you want to use has entered the Public Domain.
Creative Commons Licensed Material
Some copyright holds elect to waive some or all of their copyright in order to increase use of their works, especially if the use is non-profit. Look for images with the CC logo, and check to see if image search engines allow you to search by license type.
Fair Use of Copyrighted Material
There are exceptions in federal law for some uses of copyrighted material, especially if the use is educational, transformative, incomplete, and has little impact on future market value. Unfortunately there are no clear guidelines as to what makes up fair use, but two good practices are to check the fair use code for your discipline and to make sure that you are using only as much of the work as you need for an educational purpose.