the moment you enter united states as a student you would be having a visa, passport and a student I-20 with you and these are the inital things which are necessary for opening a bank account. it is important that you have social security number. In case you go to the bank before you get ur SSN, then they ask you to inform about your social security number as and when you get it. it is the same with signing the lease for an apartment. it might however be difficult to get a cell phone without your SSN.
another piece of advise when you are opening a bank account. you might want to open a student checking account. his would most probably be the one without any monthly or annual fees. you will certainly get most of the information from the indian students who have been there.