MickM: no worries about my time; if I didn't want to volunteer it I wouldn't be here! Plus I'm back from traveling as of today and so I should be able to respond faster.
The problem was that you didn't cd into the directory containing the files after you unzipped them. After typing "unzip RTL8188CU_linux_v3.1.2590.20110922.zip" and before typing "chmod +x install.sh" try doing "cd RTL81*" Then proceed as before. This should work.
I wish I could think of a simpler way for you to do this, or one that wouldn't require the command line, but because of the way Realtek has packaged this driver I think this is the only approach.
SlaneBoy: sorry to hear about your experience. Unfortunately wireless on Ubuntu is not always as pain-free as it would be in an ideal world--though in Ubuntu's defense, there are very many wireless devices which do "just work" out-of-the-box, with absolutely no installation of third-party drivers necessary. That's a lot better than Windows can do.
Unfortunately there is apparently no driver built into Ubuntu for your particular device (either that, or for some reason the driver exists but is not loading properly; that's unlikely, however). In most cases you can solve this problem either by installing a native Linux driver yourself, if one exists, or failing that you can use ndiswrapper in conjunction with a Windows driver. (The "invalid driver" message you received while trying ndiswrapper before usually means that you didn't install the Windows driver properly.)
To figure out what to do in your situation, we will need to know exactly which wireless chipset you have. Knowing the device name ("RTL 81922SU") is not always sufficient because often manufacturers will change the wireless chipsets while still selling devices under the same exact name (this is one of the reasons that wireless issues can be complicated for Linux users).
If you post the output of these commands they'll tell me the wireless chipset, as well as some other information that might be useful to advise you on how to get the device working:
You run these commands by in a terminal window, which you can open by pressing the keys control-alt-t at he same time, or by launching it from the Ubuntu menu.
lshw -C Network
dmesg | grep -ie rtl -e wlan