Very Obvious: check for work previously done on the author and/or MSs, in

Critical editions (of any of the author's works, not just the one you want) and scholarly biographies of the author.

Articles on the author and/or MSs: find them in
1) annually updated bibliographies
MLA International Bibliography: database, and yearly printed volumes for the years not entered.
Annual Bibiliography of English Language and Literature
Year's Work in English Studies/ Modern Language Studies
Dissertation Abstracts International: yearly listing of all dissertations registered with DAI.
Annual international bibliographies in your field, e.g. International Medieval Bibliography
2) specialist journals/periodicals: often publish annual bibliographies and/or have good indexes
 a) focusing on the period or author in question: e.g. Yearbook of Langland Studies, Mediaeval Studies, etc.etc.etc.
 b) focusing on the study of MSs of a particular period or region, or on editing:
 e.g. TEXT, Scriptorium, English MS Studies

Books on unpublished writings of a particular type, e.g. Joan Ferrante's book on medieval women's letters, Arthur Marotti's books on Renaissance coterie poetry.

Pretty Obvious: check catalogues of libraries and other MS holdings that might have your text

1) Catalogues of/guides to catalogues: e.g.
The World of Learning: *updated annually!  Lists all libraries and other relevant collections, all university departments, all over the world, *together with addresses and names of staff*.  (Of course this sort of information can often now be found on the Net as well.)
P. O. Kristeller, Latin MS Books before 1600: A List of the Printed Catalogues and Unpublished Inventories of Extant Collections
The British Library: Guide to the Catalogues and Indexes of the Department of Manuscripts
2) Specialized catalogues: e.g.
Catalogue of MSs containing Middle English Romances
Catalogue of Illuminated MSs in Oxford Libraries
3) Catalogues of individual libraries or collections: These will fill a whole room in most major research libraries, and there should be more on microfilm.

Not So Obvious:

Write to other scholars working in your area to find out the newest unpublished information.
If your MS is in private hands, check sales catalogues, e.g. for Sotheby's, for the last years its owner is known.
(Only, obviously, when the papers of a recent author have not been studied), write to the living relatives of the author most respectfully requesting help with your researches and access to any extant papers.
 

Writing to Libraries and Collections:

Remember that most MSs are privately owned, or at the very least not on public view: even though most libraries are happy to help in every way possible and to put themselves out considerably for your benefit, it's useful to remember that in writing an application, you are requesting a privilege.

Include in your letter
1) your name, rank and institutional affiliation
2) (when you are a student) the name of your advisor, and a xerox of a letter of recommendation.  (Even later, particularly when applying abroad, it's a good idea to include a xeroxed letter.)
3) a brief description of the work you plan to do, which MSs you will need, and your estimate of how long it will take.
4) a proposed date or range of dates for your visit, with the promise of a follow-up call or email to arrange the precise details.

Working with unpublished materials:

Transcription Symbols:

There are various conventional systems of transcription, just as there are various styles of bibliography and footnoting: what is important is that your system should account for all the features you encounter, and that it should be legible and consistent.  Punctuation should be transcribed just as it appears: you can decide later whether to modify or retain it.  Here are some symbols that might be useful:

^  Material inserted (between lines or in the margin)

[ ] Material deleted but still legible

< > Damaged text. Put a dot for each letter space if you can't read it; transcribe the
   text if you can read it; underline your transcription if it's conjectural.

vertue  Underlined letters are an expansion of an abbreviation.

v'tue  ‘ indicates there's an abbreviation you're not sure of how to expand.  (Usually I transcribe
  in pencil so that I can include a drawing, between {}s so it's clear it's my note.)

{ } Your own more elaborate notes on what's going on in the text.

  Bold face or different colour writing; usually a heading

 / The end of a line.

 /{b} The end of a column (and beginning of column b)

//   The end of a page.  (All three of these can be worth noting because they are frequent sites
  for scribal error.)