Copyright protects the rights of a creator to make copies of his/her own work. Facts, ideas, U.S. government works, and most work created before 1923 are considered public domain and are not protected by copyright. Copyright protection falls under Title 17, U.S. Code and covers "original works of authorship." If you do not own the copyright for a work, you must get permission from the owner before reproducing/sharing their work.
Fair Use (17 U.S.C. §107 ) makes certain uses of a copyrighted work without the owner's permission legal. Fair Use is the reason why we can quote from a book when we are making an argument in a paper, or why a professor can show a reproduction of an artwork in a class lecture. The law around Fair Use is purposely vague, so you must analyze each use against the Four Fair Use Factors, to determine if it is legal and fair use or not.
The four factors to consider when determining if your use is fair use are:
(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
(2) the nature of the copyrighted work;
(3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
(4) the effect of the use upon the potential market for or value of the copyrighted work.
The Visual Resources Association (VRA) and the College Art Association (CAA) have both issued statements on the fair use of images. Each argues that the use of images for teaching in limited-access online course sites (such as a course Sakai site) counts as fair use, but each states that as a good faith gesture, those images should have full attribution describing the artwork (title, artist, medium, size, date, owner, etc.) and stating the copyright owner.