There has been a lot of confusion on this topic. I hope to clarify this somewhat. If you have a technical disagreement with what I say, please correct me. If you cannot provide a technical reason for a disagreement, DO NOT POST IT. We do not need any more confusion.
Basically, there are 4 ways to view a wired (cat5e cable) connection. There are 2 terms that can be related in several different ways. These are Wide Area Network (WAN) and Local Area Network (LAN). One other connection type would be a client device. This is the end of the line in a network. These terms are pretty self-explanatory. How they relate to each other is not.
A client device can be connected to a LAN port from any other device. It cannot be connected to a WAN port. Depending on your client devices and the cable you use, a client can connect to another client to create an ad hoc network.
A LAN port can connect to a client device, or a WAN port on another device. It cannot be connected to another LAN port.
A WAN port can connect to a LAN port. It cannot connect to another WAN or client device.
Another way to think of this is one way flow of a stream. This is not a perfect analogy, because you can send information "upstream" when you perform such actions as email or hosting p2p. However, this analogy will give you an idea of the "chain of command" in a network. Each port must be connected according to this chain. A signal flows from a LAN port on one device to a WAN port on another device, is redirected through a LAN port on the second device, which can be distributed to another devices WAN port or to a client. A device will usually have one WAN port to recieve a signal and multiple LANs to distribute it to client devices or other networks below it in the stream.
How does this apply to the Airport Express? It has a WAN port to receive a signal and no LAN ports. Wireless doesn't need LAN ports, however, since the wireless part is actually acting as the LAN ports. The Airport Extreme does have a LAN, port, however, so that computers and devices without wireless capability can connect to the network. Airport Express skips the LAN port to make it simpler and smaller.
So how can you use an airport express? You can connect the WAN port on the aexpress to a LAN port on a network device (such as a router or dsl or cable signal) to distribute the signal wirelessly to other computers. You can connect to the aexpress with your computer by the wireless LAN signal. You can connect the aexpress to another airport base (basically, a wireless LAN port on one and a wireless WAN port on the other). You can even bridge the networks so that they are essentially one network.
What you cannot do with an aexpress. You cannot connect a client device (such as a computer, xbox, ps2) directly to the WAN on the aexpress. You must connect both devices to the LAN ports on a router in order to connect them. With some configuration you might be able to get an audio signal to the aexpress in this setup (I'm not confident about this). Alternately, you can buy a wireless bridge from dlink or linksys or whoever that will turn a wired client device into a wireless one. This is most useful for gaming consoles since it would be easier and cheaper to throw a wireless card into your computer, though I have one to connect a non-wireless capable imac to and old (graphite) basestation).
I think that's pretty much everything. If I missed some crucial point or got something backwards, please let me know.
Basically, there are 4 ways to view a wired (cat5e cable) connection. There are 2 terms that can be related in several different ways. These are Wide Area Network (WAN) and Local Area Network (LAN). One other connection type would be a client device. This is the end of the line in a network. These terms are pretty self-explanatory. How they relate to each other is not.
A client device can be connected to a LAN port from any other device. It cannot be connected to a WAN port. Depending on your client devices and the cable you use, a client can connect to another client to create an ad hoc network.
A LAN port can connect to a client device, or a WAN port on another device. It cannot be connected to another LAN port.
A WAN port can connect to a LAN port. It cannot connect to another WAN or client device.
Another way to think of this is one way flow of a stream. This is not a perfect analogy, because you can send information "upstream" when you perform such actions as email or hosting p2p. However, this analogy will give you an idea of the "chain of command" in a network. Each port must be connected according to this chain. A signal flows from a LAN port on one device to a WAN port on another device, is redirected through a LAN port on the second device, which can be distributed to another devices WAN port or to a client. A device will usually have one WAN port to recieve a signal and multiple LANs to distribute it to client devices or other networks below it in the stream.
How does this apply to the Airport Express? It has a WAN port to receive a signal and no LAN ports. Wireless doesn't need LAN ports, however, since the wireless part is actually acting as the LAN ports. The Airport Extreme does have a LAN, port, however, so that computers and devices without wireless capability can connect to the network. Airport Express skips the LAN port to make it simpler and smaller.
So how can you use an airport express? You can connect the WAN port on the aexpress to a LAN port on a network device (such as a router or dsl or cable signal) to distribute the signal wirelessly to other computers. You can connect to the aexpress with your computer by the wireless LAN signal. You can connect the aexpress to another airport base (basically, a wireless LAN port on one and a wireless WAN port on the other). You can even bridge the networks so that they are essentially one network.
What you cannot do with an aexpress. You cannot connect a client device (such as a computer, xbox, ps2) directly to the WAN on the aexpress. You must connect both devices to the LAN ports on a router in order to connect them. With some configuration you might be able to get an audio signal to the aexpress in this setup (I'm not confident about this). Alternately, you can buy a wireless bridge from dlink or linksys or whoever that will turn a wired client device into a wireless one. This is most useful for gaming consoles since it would be easier and cheaper to throw a wireless card into your computer, though I have one to connect a non-wireless capable imac to and old (graphite) basestation).
I think that's pretty much everything. If I missed some crucial point or got something backwards, please let me know.