You will need the W-2 form (more common) and/or the 1042-S (less common). Your institute will send you these forms by post mail or in a digital form. If you have been refunded of state tax in the previous year you will probably receive by post mail the form 1099-G. If you did not receive the form 1099-G or lost it, just check the exact amount of state tax refunded to you in the previous year. New: From this year (2016) you might receive a form 1095, reporting details on your health coverage in 2015. If you received 1095 B and/or 1095 C, you do not need to do anything with them, just save them between your records. If you received the 1095 A (for heath insurance acquired in the marketplace), you might deduct part of the cost of your health insurance from your tax declaration.
In order to declare your income, if you are a non resident alien (generally, first two calendar years spent in U.S.) it is preferable to refill the form 1040NR-EZ (see instructions) for federal taxes and the form 540 NR short (see instructions) or the 540 NR long (for people applying a tax treaty, married non resident alien and other situations, see instructions) for Californian State Taxes. If you refill the form 540 NR long you will also need to complete and attach to your Californian tax return the appropriate Schedule CA.
Instead, if you are a resident alien (more than two calendar years spent in U.S.) it is preferable to refill the form 1040 (see instruction) for federal taxes and the form 540 (see instructions) together with the appropriate Schedule CA for Californian State Taxes.