No one book can encapsulate all the wisdom about research methods, but this seems to me to be a useful and recent book to start with:
Research Methods in Theatre and Performance. Ed. Baz Kershaw and Helen Nicholson. Edinburgh: Edinburgh University Press, 2011. Geisel PN 2075 .K47 2011; Langson PN 2075 .R47 2011
Even newer is a collection of essays by Robin Nelson, Director of Research at the Royal Central School of Speech and Drama, University of London: Practice as Research in the Arts: Principles, Protocols, Pedagogies, Resistances. Basingstoke; New York: Palgrave Macmillan, 2013. Geisel and Langson: PN 1576 .N45 2013.
And even newer is Performing Digital: Multiple Perspectives on a Living Archive. Ed. David Carlin and Laurene Vaughan. Farnham, Surrey; Burlington, Vt.: Ashgate, 2015.
An edited collection of essays by various scholars and practitioners is: At the Intersection Between Art and Research: Practice-Based Research in the Performing Arts. Ed. Carsten Friberg and Rose Parekh-Gaihede. Malmo: NSU Press, 2010. Geisel PN 1576 .A88 2010; not in Langson.
Note: All of these are printed books.
Bailey, Claudia Jean. A Guide to Reference and Bibliography for Theatre Research. 2nd ed.
UCSD: PN 1620 .A1 B15 1983 Geisel Stacks Flooor 7
UCI: Available via ILS.
Bopp, Mary S. Research in Dance: A Guide to Resources. NY: G. K. Hall, 1994.
UCSD: GV 1584 .B6 1994 Geisel Stacks Floor 5
UCI: Special Collections, same call number as UCSD; Langson stacks: Z 7514 .D2 B6 1994
Guide to Reference Books. 11th Edition. Ed. Robert Balay; Assoc. ed., Vee Friesner Carrington. Chicago: American Library Association, 1996. Section BH: Theater and Performing Arts (pp. 714-747) compiled by the late Philip A. Smith, former Bibliographer for Theater,
UCSD & UCI: Z 1035.1 .G89 1996 Research Assistance Desk in Geisel Reference
Note: New, online-only edition was published in Summer 2008, but neither UCSD nor UCI subscribes.
Pruett, Barbara J. Popular Entertainment Research: How to Do It and How to Use It.
UCI: PN 1576 .P78 1992 Langson Stacks; UCSD use Melvyl to request.
Shaland, Irene. American Theater and Drama Research: An Annotated Guide to Information Sources, 1945-1990. Jefferson, N.C.: McFarland, 1991.
UCSD & UCI: PN 2266.3 .S53 1991 Geisel / Langson stacks.
Simons, Linda Keir. The Performing Arts: A Guide to the Reference Literature.
UCSD: PN 1584 .S56 1994 Reference
UCI: Z 6935 .S56 1994 Langson Reference & Stacks
Theatre & Performing Arts Collections. Guest editor Louis A. Rachow. (Special Collections, v. 1, no. 1) New York: The Haworth Press, 1981.
UCSD: Geisel stacks PN 1577 .T43; UCI copy at SRLF, use Melvyl to request.
Whalon, Marion K. Performing Arts Research: A Guide to Information Sources. (Performing Arts Information Guide Series; v. 1)
UCSD: PN 1584 .W47 Geisel Stacks Floor 7
UCI: Available from SRLF; use Melvyl to request.
Wilmeth, Don B. Variety Entertainment and Outdoor Amusements: A Reference Guide.
UCSD & UCI: GV 1853.2 .W54 Reference
Young, William C. American Theatrical Arts: A Guide to Manuscripts and Special Collections in the United States and Canada.
UCSD: PN 1584 .Y68 1971 Reference
UCI: Z 6935 .Y68 Langson Stacks