I struggled to get my scanner working using the instructions from williamts99 at http://ubuntuforums.org/showthread.php?t=154429 and I discovered it left out the step of adding your username to the scanner group. So here is my complete howto, based on the work of williamts99.

Where I show code like this
do some instruction here
it means you should type or copy this into a terminal.
To open a terminal,
  • search for "Terminal" in Unity,
  • select |Accessories|Terminal from your Ubuntu menu,
  • or press [Ctrl] [Alt] [T].

If you haven't already, install sane and xsane. I prefer xsane as a GUI for sane but you can use some other application if you prefer.

sudo apt-get install sane xsane
Create and navigate to driver firmware directory
sudo mkdir /usr/share/sane/gt68xxcd 
cd /usr/share/sane/gt68xx
Download driver firmware file sbfw.usb
sudo wget http://www.meier-geinitz.de/sane/gt68xx-backend/firmware/sbfw.usb
Set up /etc/sane.d/gt68xx.conf file
cd /etc/sane.d/
sudo sed -i.backup -e 's/^#override "mustek-scanexpress-1200-ub-plus"/override "mustek-scanexpress-1200-ub-plus"/' gt68xx.conf
You could also do this by editing the gt68xx.conf file in gedit or your text editor of choice and remove the # from the start of the line that looks like #override "mustek-scanexpress-1200-ub-plus"
sudo gedit /etc/sane.d/gt68xx.conf
Add your user name to the "scanner" group
sudo adduser <username> scanner
Alternatively you can do this with the Gnome Users and Groups management tool
sudo apt-get install gnome-system-tools
Then run "Users and Groups" from |System Tools|Administration (if you are using a menu based desktop environment like Gnome Fallback or Xfce)

or search for “Users and Groups” in Unity

Click "Manage Groups"
Click on the "scanner" group and select "Properties"
Tick any users who should be able to use the scanner.

If you still have problems you may (or may not) find the following links helpful

Good luck!