Create and place a favicon.ico file in the root (ie: "public_html" or "httpdocs" etc) directory of your web server, using your FTP program.
In MOST cases, that's all you need to do !!!
Note: the icon typically needs to be 16x16 px, and your graphics program needs to be able to generate .ico files suitable for this purpose.
There are other formats such as 32x32 etc which can be used as alternatives for various purposes. You can google for favicon to find more tips and tricks on generating these alternative formats.
NOTE: You will usually have to bookmark your store in order for the favicon to be cached by the browser for display. Often pressing CTRL+D will quickly bookmark the page you're currently viewing.
2. OPTIONAL: Use a different image name, or force browsers to load a specific filename (normally NOT needed):
If you wish to have each page setting the favicon data explicitly, you can simply open your /includes/languages/english/YOURTEMPLATE/meta_tags.php file and uncomment the define for FAVICON as shown:
// favicon setting // There is usually NO need to enable this unless you wish to specify a path and/or a different filename define('FAVICON', 'favicon.ico');
With that set, Zen Cart will explicitly mention the favicon settings on every page, automatically.
3. Additional information for supporting tablets and other devices: