NOTE: This is just how I did and it worked for me fine.
A favicon is that little image that shows up next to your address bar and tabs.
This is how I did it.
First make a 16x16 image and save it as a .ico. I have a plugin for my photoshop that lets me save files as icons.
There are others ways were you don't need to save it as icon or programs that save as icons but you will have to google to find them.
Make a image or shrink down one your choice. Save it as "favicon" and upload to root /public_html.
Now in the templates folder go to:
templates/default/template.html
OR what ever theme you want to add a favicon to.
Open it and find:
Code:
<link rel="stylesheet" media="screen,projection" type="text/css" href="templates/yourtheme/themename.css" />
Under it add:
Code:
<link rel="shortcut icon" type="image/x-icon" href="favicon.ico">
Now save and your favicon should show up now. I always have to close my firefox and reopen it before the image will show up.