Copyright law gives the owner of copyright a temporary exclusive right to do and to authorize others to:
Copyright owners are not required to give notice of copyright. This means it is safe to assume that anything you find online is copyrighted. Copyrights expire after a period of time. Then the works fall into the public domain, and may be freely copied, performed, displayed, etc.
Fair use is an exemption to copyright restrictions for purposes such as education and research, commentary and parody. This is why you can copy and display copyrighted works in a classroom situation. Educational fair use does not extend outside of the classroom environment however.
For basic and detailed information about copyright, see the US Copyright Office.