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. The file you created in this way will have the extension .ico. Copy the file to the /joomla/templates/<your template> directory and name it favicon.ico.
4. Open a browser. Do you see your new icon? If so, congratulations. If not, that doesn't necessarily mean you did anything wrong. Browsers are designed to minimize data traffic, so they don't refresh the favicon every time they show a page. Even refreshing the page (F5) wont help. So you need to refresh more thoroughly:
   • Mozilla / Firefox / Safari: hold down Shift while clicking Reload, or press Ctrl-Shift-R (Cmd-Shift-R on Apple Mac);
   • IE: hold Ctrl while clicking Refresh, or press Ctrl-F5;
   • Konqueror: simply click the Reload button, or press F5;
   • Opera users may need to completely clear their cache in Tools→Preferences.
   • Chrome: Shift-F5

If this doesn't work you will need to delete the temporary internet files and the history and then open your page again.

Some templates contain code that redirects the browser to another directory or another icon file. To determine where your new favicon should be, examine http://yoursite.com/templates/your_template/index.php and look for code that contains the text <link rel="shortcut icon". There you will find the directory and the name of the icon file. Copy your icon to that place and give it the the name that link is pointing to (you might want to backup the old file). Make sure you set the security correctly such that you webserver has access to that file. Look at the example below.

http://yoursite.com/templates/your_template/icon/favicon.ico" />

If you don't want to just change the favicon.ico file in its respective template directory you can find the reference to the favicon.ico file in the html.php document. The path is "........\libraries\joomla\document\html\html.php". This should prevent the icon from toggling if you use

http://yoursite.com/templates/your_template/icon/youricon.ico" />

in the template html and you don't remove the favicon.ico file. (why call the icon twice?)

From the html.php

// Try to find a favicon by checking the template and root folder
                $path = $directory . DS;
                $dirs = array( $path, JPATH_BASE . DS );
                foreach ($dirs as $dir )
                {
                        $icon =   $dir . 'favicon.ico';
                        if (file_exists( $icon ))
                        {
                                $path = str_replace( JPATH_BASE . DS, '', $dir );
                                $path = str_replace( '\\', '/', $path );
                                $this->addFavicon( JURI::base(true).'/'.$path . 'favicon.ico' );
                                break;''