There are as many different tax situations as there are people, so this is just a broad overview of some of the issues to be aware of when paying taxes as a graduate student. As far as we are aware, the money from standard TAs, RAs, and fellowships that is used to pay your tuition is not taxable. However, you are responsible for paying taxes on your stipend. If you are paid by the payroll office (if you receive bi-weekly checks or direct deposits) then you will probably have federal and state taxes withheld automatically. If you are an international student, though, this may not happen. Similarly, if you are on a fellowship, you will not have taxes withheld.
If you do NOT have taxes withheld, you need to pay estimated tax to the IRS four times a year. The estimated tax forms (which should have a name like 2006 Form 1040ES) are available online at http://www.irs.gov/(other IRS forms and publications are available here as well). If you do not make estimated tax payments, you may find yourself paying large penalties when you file your taxes in April.
The Payroll office (H7) has an information filled page with documents on how to understand your W-2, and a wealth of information about student tax issues, including issues for international students: CLICK HERE. If you have questions this is a good place to look (you'll have to scroll past links to information on staff and faculty benefits to get to the student information, but it's worth it).