I was looking to change my favicon on my website, and found a great way to generate new favicons on the web, without installing any software on your computer. Just go to http://www.genfavicon.com/ and follow his VERY easy steps.
If you would like to add your favicon to your wordpress website, you can follow this tutorial I made here
If you just want to use it on a relatively simple website, just upload it to your root directory (usually www, or public_html folder).
If you want to add your favicon to your wordpress blog, follow this link here : click!