Some readers may know that the Family History Library in Salt Lake is offering to make duplicate copies of items in its collection for patrons. There are restrictions to this service and blog readers are advised to read completely those restrictions and limitations and realize that those items apply not just to others, but everyone. [Note-update: apparently this service is for books and other materials that do not leave the library--my request does not meet that requirement as the microfilm does go out on loan.]
I've made one request myself, just to see how the service works. I get to Salt Lake annually, so I am not going to make many requests--besides I have enough things to write about as it is.
Include as much detail in the request as you have, but keep in mind that it is not necessary to prattle on about how you are related to the person, how long you have been researching for the person, how much it would mean to you to have the record, etc. Those details only make it take more time to read your request.
Read and follow (yes, follow) the directions on the Photoduplication Service page.
[Note-update: apparently this service is for books and other materials that do not leave the library--my request does not meet that requirement as the microfilm does go out on loan. Your request should be as specific as possible. ]