A good beginning search, specific to artist,  might be the Biography and Genealogy Master Index available as an electronic index (non-UNCA, password only)

For well-known artists no longer living, the Dictionary of Art (34 vols.) in Reference or available online- Grove Dictionary of Art. An excellent and authoritative source.

The Internet is also a rich and growing resource for contemporary artists. Choose a standard search engine such as Google, AltaVista, or Yahoo)  and enter the name of the artist. For artists who are no longer living it is best to use the standard print resources.  Also, be sure to consult the new Dictionary of Art (34 vols.) first, and look for the bibliographies following the article. 

Other biographical resources located in Reference, follow:

Benezit, Emmanuel. Dictionnaire critique et documentaire des peintres, sculpteurs, dessinateurs et graveurs ... 8 vols. 1948-55. Dated version, but a standard in the field.

-----------------------------. Dictionary of artists, Paris : Gründ, 2006    14 v. : ill. ; 22 cm. [NEWER VERSION OF THE DICTIONARY] 

Dictionary of National Biography. 22 vols. London: Oxford Univ. Press, 1959-60.
Use mainly for British artists and historians.

Cummings, Paul. Dictionary of Contemporary American Artists, New York:St. Martin’s Press, 1994, 6th ed

Contemporary Artists. New York: St. Martins Press, 1977- present.

Contemporary Photographers. 2nd ed. Chicago: St. James Press, 1988.

Contemporary Architects. 3rd. ed. New York: St. James Press, 1994.

Murray, Peter. Dictionary of Art and Artists. Baltimore: Penguin Books, 1962

Osborne, Harold, ed. Oxford Companion to Art. Oxford: Clarendon Press, 1970