Procedures:
1.) Fire up the installer.
2.) Click "Install", after clicking install it will give the typical "Unable To Connect" error message (you can ignore this), however notice the yellow warning icon at the bottom of this page?
3.) Click the warning image, the installer will request an "Authentication Code".
4.) This was almost too easy, simply copy one of the keys (above) for your region of SC2 (mine is "en-GB" therefore I used "G8MN8UDG6NA2ANGY6A3DNY82HRGF29ZH"), paste the code in the "Authentication Code" dialog box and click "Ok" and you are on your way to installing the game.
5.) Write down or store the code (for future reference, when installing offline).
Note: Keys are region specific...