The favicon for Joomla 1.5 templates is kept in the templates/template_name folder. The file is called favicon.ico and you can easily change your favicon by replacing this file with your new favicon file.

You can create a favicon manually on your computer or you can use an online favicon generator. Here are several such generators:

Dynamic Drive Generator

Graphics Guru Generator

1Favicon Generator

Once you create the favicon, you should upload it to templates/template_name and rename the file to favicon.ico, replacing the old one (it is recommended to keep a copy of the old favicon, just in case you wish to restore it at a later moment).

Clear up your browser's cache and your Joomla's cache (if it is enabled) and reload your website. The new favicon will appear in your browser's address bar :)

If you have problems changing your Joomla favicon yourself, ask your host for assistance. SiteGround provides the best Joomla hosting and such requests are handled with ease.