You probably need the AirPort's password, as in the device itself - not the network password.
The default password is public but you may have changed it. Try "public" (without the quotes of course).
If that doesn't work you have three choices: find the program Keychain Access - it's in your Utilities folder. Open it and search for a Keychain entry for your Express. If you type airport in the search bar you will probably find it.
Choice #2 is to momentarily depress the tiny recessed reset button on the Express. Pressing it for a half second will suffice. This will give you two minutes in which you can open AirPort Utility to change the AirPort Base Station's password. AirPort Utility is also in your Utilities folder. If you do not have it download it here: AirPort Utility 5.4.2
Choice #3 is to "hard reset" the Express in which you will have to reconfigure it from scratch. Read the following to determine how to perform the reset: