Ok, you said the file was on your desktop, which I am assuming is ~/Desktop. Please open a terminal and to do the following to install it for your user.
tar xzf FacebookPlugIn-1.0.3.tar.gz
chmod a+x FacebookPlugin_Install.sh
If there are any error messages please don't bother trying to run the reamaing commands, just post the full output to the forum.
PS. Some of the commands (ls, pwd, ls -l) are just to provide information in case is does not work.