The main branch of your local library probably has the requisite reference books and art-savvy librarians to help you figure out the salient facts. They can also refer you to appraisers and other art experts who can help you with advanced questions. An alternative is your local museum's library, but be aware that many don't welcome the general public.
To get a walking-tour of this kind of research dip into: Etta Arntsen's Guide to the Literature of Art History (Chicago: 1978) or Lois Swan Jones's Art Information: Research Methods and Resources (Phoenix: 1999).
The central branch of my city's library (Washington, D.C.'s Martin Luther King branch) has a fine art reference collection. It is also open evenings and weekends, unlike many museum libraries. "We help the customer to identify the artist, determine auction history, and make appropriate referrals," says George McKinley Martin, head of the D.C. Library's Art Division. "To identify artists we use sources as follows: Benezeit's Dictionaire des Peintures, Sculpteurs, Dessinateurs et Graveurs; Thieme-Becker's Kunstler-Lexicon; Mallett's Index of Artists; Havlice's Index to Artistic Biography: Contemporary Artists and Cederholm's Afro-American Artists: A Bio-bibliographic Directory."
Some other key sources at the library are:
Signature and Monogram Directories
Castagno, John. European Artists: Signatures and Monograms, 1800-1990. (Metuchen, N.J.: 1990).
Castagno, John. American Artists: Signatures and Monograms, 1800-1990. (Metuchen, N.J.: 1990).
It's ill-advised to rely on the signature guides alone, though they are a good preliminary step. A signature or monogram that matches the one on your piece doesn't guarantee the work is real. Like the rest of us, artists' signatures evolve over time. Forgers also go to the library and find signatures.
Dictionaries and Biographical Directories
Dictionary of Contemporary American Artists (New York: 1994).
Encyclopedia of World Art (15 vols.) (New York: 1968).
Falk, Peter H. Who Was Who in American Art: 1564-1975 (3 vols.) (Madison, CT: 1999).
Graves, Algernon. The Royal Academy of Arts: A Complete Dictionary (4 vols.) (London: 1970).
Huyghe, Rene. Larousse Encyclopedia of Modern Art from 1800 to the Present Day (London: 1965).
Index to Artistic Biography (Metuchen, NJ: 1981).
Johnson, J. and Greutyner, H. Dictionary of British Artists, 1880-1940 (London: 1955).
Petteys, Chris. Dictionary of Women Artists: An International Dictionary of Women Artists Born Before 1900 (New York: 1985).
250 Years of Afro-American Art: An Annotated Bibliography (New York: 1981).
Waters, Grant M. Dictionary of British Artists Working 1900-1950 (2 vols.) (Eastborne: 1975).
Who's Who in American Art (New Providence, N.J.: annual publication).
Price Guides
Everyone wants to know how much their treasure is worth in money. The owner undertaking research may already know what it's worth to them sentimentally, spiritually and aesthetically. You'll never truly know how much it will fetch on the open market until you try to sell it. So much depends on its condition, where you sell it, styles, and lots of other variables you can't control. But you can get a rough notion of the piece's worth by comparing it with comparable past sales. The main branch of your library may have some of these standards, which come out each year:
Hislop, Duncan (ed.). The Art Sales Index (Surrey, England).
Monod, Thedore (ed.). Mayer International Auction Records (New York).
Theran, Susan (ed.). Leonard's Annual Price Index of Art Auctions (Newton, MA).
Some sources particularly relevant for European and British art are:
Frederickson, B.B. (ed.). Index of Paintings Sold in the British Isles During the Nineteenth Century: 1801-1805 (3 vols.) (Oxford, 1988).
G. Redford, Art Sales: A History of Sales of Pictures and Other Works of Art (2 vols.) (London, 1888).
Graves, Algernon. Art Sales from Early in the Eighteenth Century to Early in the Twentieth Century (3 vols.) (London, 1918).
Next: What if the evidence is conflicting or ambiguous?
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From your Guide: Nadine Granoff, professional art researcher, locates artistic needles in prestigious Haystacks otherwise known as the Library of Congress, Archives of American Art, and the National Gallery of Art Library in Washington, D.C. She's been happily doing so for the past ten years. She may be reached at her email address.

