Here's a quick easy and fun walk through for you .... a favicon means favourites icon, when you look at my website address in the top address bar of your browser you will see my logo a little orange crown on a white background, that is my favicon.
Ok firstly generate your favicon using a generator such as www.favicon.co.uk
Once generated save the favicon to your desktop, do not change the default file name of favicon.ico
Then log into your google site, click on More Actions > Manage Site > Attachments > Click on upload > Browse > Select your favicon file from your desktop.
You might wonder what now, but that is really all you have to do!
It might take a while to refresh > sit back and marvel at your favicon when it eventually appears, I was really chuffed when I did mine, it really does look like you made it in the internet world!
Any probs let me know.