Images published in either print or online sources are covered by the Copyright Act of 1976, an Act for the general revision of the Copyright Law, title 17 of the United States Code. Copyright law provides protection to the authors of "original works of authorship," including literary, dramatic, musical, artistic, and certain other intellectual works.
Section 106 of the Copyright Act generally gives the owner of copyright the exclusive right to reproduce, distribute, perform, display or make derivitive works from their original work. In addition, certain authors of works of visual art have the rights of attribution and integrity as described in Section 106A of the 1976 Copyright Act. See Circular 40, Copyright Registration for Works of the Visual Arts.
Limitations to the restrictions on use of copyrighted works have been established in Fair Use guidelines, Section 107 of the Copyright Act based on consideration of four factors. It is important to realize that the "four factors" guidelines do not precisely clarify legality of uses of copyrighted works. Whether or not you are within the boundaries of fair use depends on the facts of your particular situation. Consult the Columbia University, Copyright Advisory Office website for further explanation of the nuances of Fair Use. Stanford University Libraries also has a good website on copyright and fair use.
A good general rule of thumb in using images you find either in print books and articles or on the internet is to read the fine print, i.e., find out the particular restrictions on the use of image, if any, and then make every effort to comply with the wishes of the creator of the image.
As a creator of original works of art (designs, photographs, etc.), you should understand and exercise your rights as well. See the U.S. Copyright Office website for full information on copyright registration.