My first stop was to consult the list of supported hardware. This was initially encouraging as it lists the WG111v2 as supported but sadly my WG111T uses a different chipset. This page also links to an example of getting an arbitrary USB wifi device working. This suggested I look for firmware on the linuxwireless.org site. Google suggested that I needed the ar5523 firmware. The change log for this firmware isn't very encouraging as it refers to the kernel panicking when the device is probed. Furthermore it's not clear how I would build and install this firmware.
More googling turned up a wiki page which described in much more detail about how to build and install the firmware. Following these steps I got as far as "dpkg-buildpackage -us -uc" before hitting an error that my version of debhelper was too old. Thankfully I was able to use apt-get to force an upgrade to an appropriately newer version. This got me as far as running "m-a a-i ar5523" where I hit the following error: