If you're interested in doing research on a musical, the New York Public Library for the Performing Arts has an embarrassment of riches. To find all the information we have, you may have to look in many different places. Of course, your first move should be to consult with the knowledgeable staff at the 2nd Floor Drama Desk, who'll be able to guide your research.
As a way of providing a guide to doing research in general, I'll take a case in point, one of the great musicals, which NYPL has covered from every angle; John Kander and Fred Ebb's 1966 masterpiece, Cabaret. You should always make sure to have the basics covered first. In NYPL's circulating collections you'll find the original cast recording, and other major recordings, the DVD of the Oscar-winning film version, and the published script, Cabaret: The Illustrated Book and Lyrics.
There are also plenty of books where you can read about Cabaret, like Open a New Window: The Broadway Musical in the 1960s (Mordden, 2001), Colored Lights: Forty Years of Words and Music, Show Biz, Collaboration and All That Jazz (Kander, Ebb, 2003) and The Making of Cabaret (Garebian, 2011).
Once you're familiar with the basics, you may wish to delve deeper into primary sources. I'm an archivist, so my main focus will be on archival collections. Also, you can start this part of your research from home. The best way to search just archival collections in the catalog is with this search tool.
From your search results, you can peruse the finding aids of these collections (From the "Location" tab on the catalog record you can find out if the collection is stored on or off-site—this is very important, because off-site materials must be requested in advance of your visit to the library.) Here are some archival collections we have relating to Cabaret, several of which I was fortunate enough to process myself:
Jack Gilford, Jill Haworth, John Kander, Fred Ebb and Joel Grey during rehearsal for Cabaret,
For information on the process of creating the text of a musical, your best bet is looking at the papers of one of the authors. For Cabaret, we have the papers of the lyricist of, Fred Ebb. Materials on Cabaret in the Ebb Papers include: scrapbooks on all major productions and the film adaptation; scripts, including early drafts with different songs and annotated drafts with notes on revisions and blocking for the original production; the bound conductor score and piano/vocal scores and published sheet music for individual songs (including several cut songs).
As director and producer of the original production of Cabaret, Prince has different types of material than Ebb. Prince's production files on Cabaret focus more on casting and producing. There are folders of head-shots and resumes for the entire ensemble and replacement casts.You can also expect to find contracts, royalty statements and box office ledgers. And there's plenty of information on the national tour and foreign productions as well.
Joel Grey originated the leading male role of the Master of Ceremonies, toured the country in the show, and subsequently reprised the role for the film version and a 1987 revival. His papers are chock full of Cabaret stuff, and they can teach us about the show from an actor's point of view. They include contact sheets, casting files, contracts, costume plots, photographs, publicity files, scripts and a wonderful souvenir gift, a memento key (labeled "Ze Key," in tribute to a lyric from the show) given to Grey by his "Two Ladies" co-stars when he left the show.
Hal Prince's frequent stage manager, assistant director and assistant, Ruth Mitchell has something else to offer in her papers. Acting as both a producer and as the production stage Manager on the original Cabaret and as Prince's Assistant Director on the 1987 Broadway revival, Mitchell's papers have agreements, costume, hair and prop photographs, correspondence, clippings, cast lists, schedules, and scrapbooks. Most importantly, Mitchell's papers contain her stage manager scripts with blocking cues, one of the single most valuable aids to understanding Prince's staging.
The legendary scenic designer Boris Aronson's papers and designs also have a lot to offer. As the designer of the original production, his collection includes research photos from the 1920s and 1930s and photographs of a model set. And best of all, there are designs, elevations, and model pieces from the famous set.
Cabaret's original costume designer Patricia Zipprodt's papers and designs also have a lot of materials on Cabaret, such as correspondence, contracts, clippings, and photographs. The most unique materials in her papers are her original costume design sketches, with fabric swatches.
A key element to any theatre research will always be photographs. As I mentioned in my descriptions of the archival collections mentioned above, many of them contain various photographs of Cabaret. But for the most comprehensive look at any show, you should consult the photograph files. The only way to search and request these is through the physical card catalog, located on the 2nd Floor of LPA. When you search the alphabetical sequence of titles, you'll find cards representing folders of photographs of multiple productions of Cabaret. (The Clippings files are also accessible by card catalog only.)
Now that you've read and seen practically everything concerned with Cabaret, the only thing left is to see the show itself. If you're a qualified researcher, you can do this at the Theatre on Film and Tape collection! (The Archive is available to theatre professionals, students, or researchers with work or study-related reasons for viewing.) A recording of the 1987 revival of Cabaret with Joel Grey, filmed at the Minskoff Theatre on May 31, 1988 and a recording of the 1998 revival with Alan Cumming and Natasha Richardson, filmed at the Kit Kat Club, on July 1, 1998 are both available.
Good luck with your research!