Federal grants such as Pell Grants are administered through the federal government and help students pay for undergraduate degrees and some professional degrees. To determine eligibility fill out a FAFSA (Free Application for Federal Aid). Grants for graduate students can be sponsored by federal agencies or institutions. Visit Gov.Benefits or go directly to the federal agency website.
Fellowships are similar to grants in that they don't have to be paid back. The most common fellowships are portable and institutional fellowships. Portable fellowships can be awarded by the federal government or by an institution. They have more flexibility in scope and give graduate students the choice of where to study. Institutional fellowships are granted by the college of university where a student has been accepted.
Private or public foundation grants extend additional funding opportunities for graduate students. Online resources like the Foundation Center and Peterson's Financial Aid Center provide links and information on these grants. Also, the National Academies has listings of available grants for graduate and post-doctoral study in science, engineering and medicine.
Assistantships come in the form of stipends and cover portions of a student's educational expenses in return for their employment within the university or college. Employment usually involves teaching or research work.
When investigating funding sources for graduate school, be sure to discuss your options with faculty members and conduct a thorough research of resources in the school library. The Council of Graduate Schools has an online list of funding opportunities which includes fellowships and scholarships.