The simplest way that wouldn't require too many changes is just to use an Ethernet game adapter for Xbox 360 / Playstation 3 etc. They act like a wireless/wired bridge between Ethernet and wireless.
For example:
TRENDnet TEW-647GA
http://www.newegg.com/Product/Product.aspx?Item=N82E16833156258&nm_mc=OTC-Froogle&cm_mmc=OTC-Froogle-_-Network+-+Wireless+Adapters-_-Trendnet-_-33156258
All you would have to do is configure the bridge. I have used this with my development boards.
Some pocket routers have this ability too such as the D-link DWL-G730AP
http://www.amazon.com/D-Link-DWL-G730AP-AirPlus-802-11g-Wireless/dp/tech-data/B0002Z45DQ
The "Cookbok" suggests using a WiFi modem to interface mbed to WiFi. However there are no low cost WiFi modems. Most cost US$75.00 or more and include a router. Whereas there are available USB to WiFi adapters, also called WiFi dongles, for less than US$25.00. However, They come with drivers for Windows, Linux and OS X. Hence I am looking for information on to use a WiFi dongle with mbed or how to write a driver so a WiFi dongle may be used with mbed.
Or a better approach would be using a WIFi transceier if one was available in the same price range as a Zigbee tranasceiver. Please post a link if you know of a source for a low cost WiFi transceiver.
Howard