I've recently been awarded an NSF-GRFP, so here's some advice on what worked for me in my application!
To preface, funding is everything in academia. You can have a brilliant idea that will shake the fundamentals of our understanding of biology, but if you don't have the money to do the experiment, the idea will have to remain in your head.
Your funding for graduate school usually comes from three sources: the department, your advisor, or externally. Departmental funding is usually in exchange for teaching: you TA a class or lab, and the department pays you. You will most likely teach unless your advisor can cover you or until you get a grant from a funding source outside of your university (e.g. the National Science Foundation, the Environmental Protection Agency, etc.). While teaching is immensely rewarding, it also takes up a lot of time. It's not just the actual two hours a week where you're standing in front of the students. It's that and the five hours a week preparing for the lab (e.g. writing quizzes), one hour setting up before lab and one hour answering questions after lab, the three hours attending lecture, the two hours in office hours, and the three hours grading quizzes. And don't forget the eight hours spent proctoring and grading exams three or four times a semester.
The requirements add up! It's hard to focus on getting any research done when so much of your time is devoted to teaching. If you're lucky, your advisor has money to cover your living expenses in addition to the costs of research. But, you shouldn't expect your advisor to have the money to shell out on you as soon as you arrive (or when you first e-mail them about working in their lab). And the money your advisor would have to spend on you would come from an external grant that he or she applied for anyway.
Even big-name professors have to secure grants to help fund their research, so the earlier you start learning how to effectively write funding applications, the better. As a graduate student in the U.S., the National Science Foundation Graduate Research Fellowship (http://www.nsfgrfp.org/) is one of the biggest sources of external funding for your research. The fellowship is a three-year stipend of $30,000/year as well as $10,500/year cost of education allowance for tuition and other fees. Essentially, this means that you come as nearly free labor for your advisor and your department - because your living expenses and tuition are covered, the money that would have been spent on your stipend can now be devoted solely to research expenses. So, instead of spending only six weeks at your field site in summer, you have the ability to spend ten weeks, for example, or you can present your research at a conference in Spain instead of in Indiana (no offense, Indiana). While you will most likely still teach for at least a year, because you have external funding, throughout your PhD you will be able to focus more on your research instead of splitting your attention between your work and your students.
Aside from letters of recommendation and your transcript, the GRFP application has three essays: personal statement, previous research experience, and proposed research. [Note: The personal statement and previous research experience are now one essay. 9-30-14] I've heard it's good to structure your essays as a cohesive whole (like a three-part story that shares themes), as the reviewers apparently read all three of your essays one after the other. So, what this means is that something like your broader impacts ideas should be woven into all three essays, not just your research proposal. Find a way to link your research ideas with ways that will benefit the local community (e.g. employing undergrads or high school students in data collection), and if not, be willing to spread your message beyond the academic sector in other ways.
One of the most important things in academia is learning how to make an argument for why what you're studying is important. If you strike up a conversation with me trying to convince me that your experiment on naked mole rat social structure is important, you don't have to try hard because I already think it's a cool topic (eusociality in a mammal?? So awesome). What's harder is when I'm a geologist on a funding panel trying to decide who should get a huge grant and I don't have the patience or time to read up on why I should care about mole rats. Ultimately, being able to convince someone else why your work is important is the key to any successful application. To do this, I recommend the following:
- Explain why your project is interesting!
This might sound obvious, but it's easy to forget to include details that we've long ago accepted but will be new to the reader. Give solid, easy to visualize reasons why your project is interesting. Don't lose your reader in jargon. "Naked mole rats are eusocial" is super interesting to an animal behaviorist, but scientists from other disciplines will most likely not get it. Try something like: "Naked mole rats present an enigma for the study of eusociality, or the highly detailed social caste systems otherwise only found in Hymenoptera insects." Then, tie it to a broader question. "Studying information transmission in groups of eusocial mammals can yield insights into human social networks."
- Be as specific as possible, whenever possible
It's one thing to say that your research will have implications for the medical sector, conservation, etc. It's another thing to say how your research will have an impact. If you end up modeling the protein you set out to do, how exactly would this make it easier to fight diabetes? If you discover the plant community composition of Jurassic-era Asia, what will this teach us about the effects of deforestation on wildlife today? Pretend your reader has no imagination and can't visualize anything unless you write it explicitly in your application.
- Be willing to do more than just research as a grad student
An NSF-GRFP is a lot of money. It's a hefty sum because it's meant for you to be largely free from financial restrictions as a grad student. NSF doesn't want to award someone who will stay in his cubicle and read papers all day. They want someone who will volunteer to give presentations on her research at the national park in which she collects moss samples, or someone who will walk into a high school and tell a chemistry class why protein modeling is cool. Sounds intimidating? Sure. I'm a bit nervous about this, too. But you should view this as an opportunity to do something really cool because you're not tied to a strict teaching schedule to earn your paycheck.
And then, of course, go through as many drafts of your essays as you can. Get feedback from your advisor, from older graduate students, from as many perspectives as you can. The NSF-GRFP comes from taxpayers' dollars, so from reading your application, they should agree that you should get the funding!
To conclude, here's a relevant post on reddit from "grfppanelist" (undoubtedly a pseudonym) on his/her experiences working for the GRFP review board and recommendations for applicants. (r/AskAcademia, topic "AMA: I used to work at the National Science Foundation")
I was on a GFRP review panel several years ago. The process at that time was to gather a panel of reviewers (mine had about 15 people on it) for a two-day review session. Each application was read by at least two panelists, who scored it for (a) intellectual merit (basically grades, GRE scores, and research proposal) and (b) broader impacts (e.g. diversity, community outreach or education plans, etc). It is critically important to understand that these two scores receive equal weight in determining the final ranking of the application. You can have a perfect GPA from MIT, perfect GRE scores, a novel and well-thought-out research plan, and letters that say you walk on water, but if broader impacts are not evident from your application you will not rank high enough to be assured of getting a fellowship.
Once all of the applications have been read (some get read by additional panelists if there is disagreement on the scoring) all of the applications are ranked by the total score. As I recall something like the top 15% was more or less guaranteed a fellowship, with another 10% or so still in the running to get an award. My impression was that in this second category the program manager applied additional criteria (e.g. whether the applicant was from an under-represented group) to decide the final awardees.
The take-home message is that if you want to win one of these awards, you need to be sure the broader impacts part of your application is convincing. It helps a lot if you have done some sort of outreach during your undergrad career and write something convincing about how you will carry similar activities forward in your graduate and post-graduate career.
[7-2-13 edit: I just found this incredibly helpful website by a former GRFP awardee. Great source of application advice.]