The "Extend a wireless network" setting mentioned in other posts in this thread will not work unless you are connecting to another Apple wireless network.
Download and install AirPort Utility 5.6 for Mac OS X Lion . You can keep both AirPort Utility 6.x and 5.6 on your Mac and use the version that you need.
Perform a Factory Default Reset on the AirPort Express as follows:
Power off the Express and wait a minute or two
Hold in the reset button on the Express and keep holding it for an additional 9-10 seconds while you simultaneously plug the Express back in to power
Release the reset button and allow 40-45 seconds for the Express to restart
Temporarily connect an Ethernet cable from your Mac to the Express
Open AirPort Utility 5.6 select the Express and click Manual Setup
Click the Base Station tab below the row of icons to assign a name and device password to the Express and adjust Time Zone settings
Click the Wireless tab and adjust as follows:
Wireless Mode = "Join a wireless network". You may need to hold down the option key on your Mac while you click on the Wireless Mode selection box to locate the "Join" setting.
Wireless Network Name = Same name as your main wireless network
Enter a check mark if you want to be able to connect an Ethernet device to the Express
Wireless Security = Exact same setting that your main wireless router is using
Wireless Password = Same password as the main wireless network
Click the Update button.
As soon as you see the message that the settings have been stored on the Express close AirPort Utility and disconnect the Ethernet cable
Wait 40-45 seconds for the Express to restart. If your settings are correct you will have a green light on the Express. You can now locate it where it will be needed assuming that it will be able to receive a good wireless signal at that location.