Do not plug the adapter until after the drivers are installed.
Download the Windows drivers from here: http://www.tp-link.com/english/soft/2007116174835.zip
Unzip 2007116174835.zip to your desktop
Open the 'Ubuntu Software Center' from the Application menu and search for 'ndiswrapper'; when found install the 'Windows Wireless Drivers' application.
Execute 'Windows Wireless Drivers' from the System -> Administration menu
After authenticating, choose 'Install New Driver' button.
Vector to the location where you unzipped the drivers in step 3 above and choose the net5523.inf XP driver.
After the driver installs you should see it displayed in the 'Currently installed Windows Drivers' list.
Plug in the adapter to a USB port and close 'Windows Wireless Drivers' app.
Open a terminal and type:
$ sudo ndiswrapper -l
net5523 : driver installed
device (0CF3:0002) present
Should echo back the above.
$ sudo modprobe ndiswrapper
Should activate the adapter, check that the LED is flashing slowly
Click on the network icon on the top menu bar and if it worked, you should be able to select a wireless network.