As a graduate student you are encouraged (although not required) to apply for graduate fellowships from organizations such as the National Science Foundation, the Department of Energy and the Department of Defense. Most fellowships are open to graduate students in their first year, but many are open to more advanced students as well.
The Office of the Dean for Graduate Education has a helpful resource to find fellowship opportunities.
Many countries offer fellowship programs for their citizens to study abroad that may not be listed here. International students should be sure to look for these as well.
For all fellowship information, please visit the Office of the Dean for Graduate Education website.