International students are taxed on income from American sources. You may also have to pay tax to your home country the American income, depending on your country's tax laws.
In general, this article has a good summary: http://en.wikipedia.org/wiki/Income_tax ... ted_States
(Scroll to the 2013 tax rate table).
As a non-resident, we can only claim the personal exemption of $3900, but NOT the "standard deduction" of $6100.
So, here is an example for a single student (or a married student whose spouse is not American)--let's say your funding package is $28,000 per year plus tuition waiver. You are not taxed on the tuition waiver. A quick way to compute your tax owing is to first deduct the personal exemption, so
$28,000-$3,900 = $24,100 of taxable income.
You can reduce this number further if you spent some of your income on mandatory materials for schools. For us, it's probably just textbooks so let's say you spent $300 on textbooks AND you kept all the receipts and claim it properly, then your taxable income is now:
$24,100-$300 = $23,800 of taxable income.
Now we can apply the tax brackets. In 2013, you pay 10% on the first $8925 of income, which is $892.50 of tax. You then pay 15% on the rest of your income (since you don't have more than $36k of income to jump into the next tax bracket), so this is ($23,800-$8,925)x0.15 = $2,231.25.
In total, your tax owing is $892.50 + $2,231.25 = $3,123.75.
If you look at your total income, $3,123.75 / $28,000 is an average tax rate of about 11%. This is just federal tax though, you may also have to pay state taxes which is about a few % depending on your state.
In general, most international grad students will pay about 10% to 15% total in taxes, with an average around 12%-13% I think.
Notes: Graduate students in America do NOT pay "FICA" taxes, which are for Social Security and Medicaid, which can add another 5% or so (I forgot the exact number). However, if you have a spouse that is on J-2 and can work, he/she will have to pay this tax as well (my spouse pays about 18% in tax). In addition, if you have a non-resident spouse, you MAY NOT file your taxes together as a family and pool your tax credits. Instead, you must file individually which usually means a less ideal tax situation.
Finally, even though you might only owe 11% of tax in the end, some schools will withhold the maximum amount of tax just in case and then you only get this money back each Spring when you file a tax return. My school withholds 14% of my income in tax and then I get a few of hundred dollars back each year. So if you are making a budget, plan on not having access to up to 15% of your income.
Now, how to reduce taxes?
There's not many ways and not much you can do about it. Most of these things are policies already in place that you have no control over:
1. Your home country might have a tax treaty with the US so that you don't pay US tax on some parts of your income.
2. Your fellowship might be a special one that is tax exempt (pretty rare).
3. If you have funding from non-American sources, as a non-resident of the US, you do not pay tax on international/foreign income.
For me, I have some funding from my home country so that #3 reduces a lot of my tax liability. It doesn't cover all of my stipend so I have some US income too, but in the last year, the US part of the income was low enough that #1 applied so I ended up paying only a small amount of tax.