Extending the range of your AirPort network using a Wireless Distribution System
Or... If you want to share the connection wirelessly (it all depends on your current network), you can use WDS, and you would make the AirPort Express a remote base station.
Essentially, a main base station is connected to the Internet and shares its connection with remote and relay base stations, A remote base station shares the main base stations Internet connection, and a relay base station shares the main base stations Internet connection and transfers the connection to other remote or relay base stations.
I believe this would result in a slower network than my first suggestion however.