For the sake of simplicity, this article assumes you are using an already created image for your icon.  Please note that forclarity the image you select for your favicon should be a square.  Remember it will be reduced to 16 x 16 pixels and non square images will become distorted.

For the purpose of this article I will be craeting a Favicon from the title image, the F and P taken from my web Design company logo.

Main Logo
                                                           Square Base Favicon image
                                                                      Final Favicon 

1. Create a .jpg image, remember this must be a square image to avoid distortion.  I have cropped the F & P from the Fiery Phoenix logo, as you can see above. 
2. The image does not need to be small - the image I use is 58x58
3. I use a free tool called Dynamic-Drive -FavIcon Generator, which makes the creation of favicons a doddle.
4. Once at the Favicon Generator wesite select the Browse button to locate the image you wish to convert to a favicon.
5. Click the Create Icon button.
6. The site will provide a sample image of the new favicon in a dummy web browser bar
7. If you like it then select Download FavIcon button to save a copy, if not then select another image and start the processover until you are happy wiht the result.

For more information on how to use a favicon we have the What is a Favicon? and Adding a Favicon to your Website in seperate articles, also if you are looking for  How to add a Favicon to Joomla 1.5 that will be covered in a future article.