Update: Previously I had linked to a blog posting by Jonathan Wylie and his site educationtechnologyblog.com. Unfortunately the posting has been taken down. In response I have posted on my blog the step by step directions for creating a favicon on your Google Site. Click Here to visit my step by step directions.
When I create my favicons I use the site: http://www.favicon.cc/
I host my site on bluehost, I like them because they have great customer service and it is easy to install open source installs such as Moodle, WordPress, etc… To create a favicon on bluehost I have to go into the cpanel, go to the file manager (html public) and open the folder that contains the website I want the favicon to appear in and save the .ico file in that folder (overwrite the old one if one is already there).