Your letter should be succinct, stately explicitly the purpose of your letter. If the organization accepts phone calls, phoning may reduce the amount of time sending, and waiting, to receive postal service. When you call, simply ask for an information packet and application materials. The organization will most likely send you a packet which will tell you more about the philosophy of the organization as well as exact eligibility requirements and deadlines associated with their fellowship and scholarship programs. A formal application will also most likely be included.
Many organizations even have websites with significant amounts of information.
Website info is also often more up to date than any reference book and often replicates any pamphlet the organization would publish. See the attached brief list of websites which are most appropriate for graduate students in the social sciences. When you have gotten in contact with the organization, they will most likely send you an application form. The Office of External Funding keeps on hand application forms which are from the National Science Foundation, The Fulbright, and The Fulbright-Hayes Foundation. Simply looking at blank application forms can show you that the application process is a long and tedious one of assembling many different materials, including references and transcripts, in addition to the thought needed to form a coherent project.