I have a LAN network with three computers connecting to the Internet both through wired and encrypted wifi connections. Is there a way I can check who is connecting to the Internet via the wifi connection?
On the wireless routers I'm familiar with, there is an admin page that lists the MAC addresses of devices that are connected. Take this with a grain of salt: a malicious user could easily change the MAC address (to either look like one of your devices, or so that it appears to be a completely different device each time he connects).
In general, most wireless routers will offer an admin page as per @bstpierre's answer. An alternative on higher end routers is to use SNMP (have a look at this blog post for some information) - which can make it easier to script for automated stats/alerting.
1Of course, this requires that all of the computers on your network are under your administrative control.– IsziDec 20, 2011 at 13:42
It would help, although even just pulling off the router info through SNMP could be informative.– Rory Alsop ♦Dec 20, 2011 at 13:44
It might be helpful to know the purpose of the connection data. The AP will have logs, you could poll the computer's interfaces for activity, or you could set up a monitor on the wifi.
Cace Technology (now Riverbed) has Cascade Pilot that can be used (with a wireless packet capture nic) to monitor wifi activity. That way you can know who is connecting, even if it is not those 3 expected hosts. There are also built-in reporting and monitoring features.