The amount of detail you need to provide in a request letter will depend on what you are seeking and from whom you are seeking it.
If you are asking a colleague for permission to share an article (to which s/he holds the copyright), a brief letter or email may suffice. If you are writing to the author, you may want to comment on the value of the work, and your reasons for sharing it. (Consider the sort of letter you would want to receive from a colleague who wanted permission to use one of your works.)
This model letter below assumes that you lack the sort of relationship that would permit a more personal letter and that the person to whom you are writing (quite possibly a publisher) will need detailed information in order to identify the work at issue.
[Author or Publisher and address] (Copyright notice will normally tell you who has the authority to provide permission).
I am writing to request permission to copy [identify work or excerpt to be copied] for use in my class, [name of class], during the _________ semester. [Or explain other purpose.] A copy of the article [or “excerpt and copyright page”] is enclosed. [Unless all of this is clear from the enclosure, you should identify: (1) the author’s, editor’s or translator’s full name(s), (2) the title, edition and volume where applicable; (3) the copyright date, (4) the ISBN/ISSN number, if known, and (4) the exact page numbers or images you wish to reproduce.]
I anticipate an enrollment of approximately ___ students in the course and wish to provide a copy for each of them. [Or, “and wish to place a copy of your work in an electronic reserve, password protected so that only these students may retrieve it.”] [If applicable: “The students will be charged only for the cost of reproduction.” OR “We would provide these copies to the students without charge.”]
[Please let me know if there is a fee for reproducing this work in this manner.] [I appreciate your assistance.]
Very truly yours,