Joomla! Documentation™

1. Create a 16x16 pixel image. You may use graphic software such as Photoshop, Gimp or Windows Paint or an online tool such as http://antifavicon.com/
2. Convert to ico format using free online sites such as: http://converticon.com/, http://www.favicongenerator.com/, http://www.htmlkit.com/services/favicon/, http://tools.dynamicdrive.com/favicon/, http://www.favicon.cc/
3. Copy the file to the folder outlined in the path above.
4. Make sure the file name is favicon.ico.

Alternatively, modify the index.php for the template, so that it uses your preferred name.ico file.