Fair Use is the use of copyrighted infringement without needing to get permission for it, for example, quoting song lyrics or summarizing an article. Another example you may utilize fair use is citing quotes from a book to use in an essay assignment for school.
In 2009 Shepard Fairey was proven guilty in court as he used an image by The Associated Press without copyright permission. With many obstacles overcame and time, Shepard and The Associate Press settled the suit for $1.6 million.
Public Domain is a work that has no or an expired copyright license. These works don't need any permission to use. Creative commons is a non-profit organization that allows sharing different works with free legal tools. They provide licenses that allow you to add your own conditions to how your files can be shared.
Halloween before image used with permission, Creative Commons.