Most banks in China are local ones, but US ATM cards usually still fit into them and students have no problem with drawing money most of the time. The only two American banks we found in Shanghai were HSBC and Citibank, both of which have ATMs at Cloud Nine Mall near NYU Shanghai’s off-campus apartments.
Before you leave, speak to your bank about (1) the high fees they may charge for overseas use and (2) not flagging your account as fraudulent due to the overseas use. To counter the large fees, some students took out large amounts of cash at one time (ATMs in China give out money in 100 RMB denominations). If you choose to do that, be careful with your cash.
Credit cards are only accepted at big restaurants. You can use them at ATMs that accept your carrier, though.