If the play has been published as a script, book, or generally as a single volume patrons can search by:
Title (Cat on a Hot Tin Roof, Oresteia, etc.)
By Author (Williams, Tennessee, Aeschylus, etc.)
Or for all library holding in main for a specific publisher choose a keyword search. MSU Libraries currently recieves the entire output of Dramatists Play Service, so patrons may try kywd: Dramatists Play Service (and limit to Main Library in the drop down menu).
To find plays by number of characters, sex of characters, and theme go to the Playfinder on the Dramatists Play Service web site: http://www.dramatists.com/ and then search by title in the Library catalog
To find monologues search the Library Catalog for keyword: monologues (with that particular spelling). A subject search for monologues will produce more pointed results. Monologues and scenes for acting auditions and the like can be browsed by going to call number range PN 2080 on 4E of the Main Library.
Also: To watch full length plays, streaming online go to Theatre in Video.