Basic Production Information
Typically, you can find out most of the basic production information by looking at the film's credits. Otherwise, you might consult reference works and databases to establish this information. If you are studying classical Hollywood films, the standard source is the American Film Institute Catalog of Motion Pictures Produced in the United States. This massive work appears in several volumes, some of which are available at Coates Library. The Library also holds several other filmographies, databases, and other reference works. For credits, release dates, and other details, you can usually find reliable information online at the Internet Movie Database.
Note that basic production information is just a first step in the research process. The IMDB is a good resource, but a solid research paper will almost certainly need to consult additional, more scholarly sources.