Make sure you meet the criteria: that you are a woman, an American citizen, and that you are an undergraduate majoring in physics, chemistry, biology, meteorology, engineering, computer science or mathematics.
Keep in mind that financial need doesn't matter. Neither does race, age, religion or ethnic background.
Check to see if your university is either a "designated institution" or an "invited institution" that receives funds for the fellowship. If not, then you aren't eligible to apply.
Contact your university's financial aid and/or scholarship office for specific information on application procedures, as the scholarships are administered on a campus-by-campus basis. Deadlines and supporting materials also vary by campus.
Notify professors and TAs well ahead of time about any letters of recommendation you'll need from them.
Apply well before the application deadline to avoid the risk of missing it.