Fellowship opportunities may reduce your teaching assistant duties over the next few years. Many fellowships also offer a stipend higher than the department pays for TAs. These are great opportunities, and you are encouraged (although not required) to apply. Most are open to graduate students in their first year, but many are open to more advanced students as well.
External Fellowships - The Office of Graduate Education has a helpful resource to find fellowship opportunities.
Fellowships for International Students - Many countries offer fellowship programs for their citizens to study abroad. Not all of these are listed at the link above, so international students are encouraged also to consult with their countries' governments.
NSF Graduate Fellowship Program - US Citizens in their first or second year should definitely apply for the NSF Graduate Fellowship Program, which usually closes in late October.