This page contains advice for applicants to the NSF Graduate Research Fellowship Program.
There is already a wealth of advice available. The website of Alex Hunter Lang was invaluable to me while writing my application. Besides containing detailed advice and links to further advice, it contains a table of previous successful applications across disciplines. I think the most useful piece of advice is: read previous applications. This is the fastest way to understand what a successful application looks like.
The editing process for a grant application will be lengthy. Four mathematicians gave me comments on my application, two of whom had previously worked for the NSF reviewing grant applications. Another was my research mentor for the project upon which my proposal was based. It is important to get feedback from both specialists and non-specialists in your particular research area; your application will be read by scientists in your general subject area (e.g. mathematicians), but not necessarily in your specific topic area. If you are writing about algebraic geometry, keep someone who works in partial differential equations in mind.
I was awarded the GRFP during my senior year of undergraduate studies. For undergraduates, the second most useful piece of advice is: the GRFP “funds the person, not the project.” What you write about in your proposal need not be what you study in graduate school. Instead, write about something that you know well. The NSF is looking for the ability to write a good research proposal. You must be able to demonstrate understanding of a problem and its context, as well as demonstrate its broader relevance. I wrote about my undergraduate research, as I was best able to meet these criteria with it.
I am willing to read and provide comments on applications on a limited basis, particularly for those who do not have access to other experienced application readers.