Do you know the model of the adapter? And can you please go to Applications -> Accessories -> Terminal in the menu, type the following commands into the terminal that appears, and post the output here?
ifconfig
lspci
lsusb
That might provide us with some useful information about your system :)
Using a native Linux driver for your wireless adapter is usually the preferred alternative, but in the event that we should not find a suitable one, you should know that it is also possible to load the Windows driver in Linux; this page might provide more information:
https://help.ubuntu.com/community/WifiDocs/Driver/Ndiswrapper