I am currently using WordPress 3.1.2.
In your WordPress Dashboard click on Apperance and more options will flow down. What you are interested in is the Editor section. The file you will be changing is the Header (header.php). Between the <head> and </head> tags you will need to include the code below if it’s not in there already:
<link rel="shortcut icon" href="<?php bloginfo(‘stylesheet_directory’); ?>/favicon.ico" />
I assume that you already made a favicon.ico file. You will need to upload this file to two locations through ftp (webmaster’s control panel – file manager). The first location is the root folder of your domain (eg: http://www.sherwinjtb.com/favicon.ico). The second location is in your current theme’s folder (eg: http://www.sherwinjtb.com/wordpress/wp-content/themes/leathernote/favicon.ico).
If you don’t have a favicon.ico file yet you can convert any image (usually .png) of size 16×16 pixels by doing a quick online search. You could also find a program that converts or saves files as icons. Microsoft Paint may save your file as an icon. In Paint, save as a 24 Bitmap image and make sure to add .ico at the end of the file name (ie: favicon.ico). Keep in mind that you want to be original so try making your own design. Find your saved file and upload to your site as stated in the locations above. This is what I did and it usually works instantly or restart your browser for it to take effect.