Momentarily depressing the Express's tiny recessed reset button will allow you to bypass any passwords that may be set so that you can reset its password using AirPort Utility, if one has in fact been set. Do not hold the reset button depressed for more than a second or so because that will erase everything and you will have to reconfigure all its parameters.
This is called a "soft reset". After the "soft reset" you have about two minutes to open AirPort Utility and start reconfiguring it, after that the Express automatically reverts to its normal state.
If you have a Mac the wireless network password is stored in its Keychain, and you can use Keychain Access to reveal it. I do not know where a PC stores the password.