I'll use my current sig image as an example. Using the following code:
[url=www.google.com][IMG]http://i32.photobucket.com/albums/d38/V3rg1l9/Sets/saix1copy2.jpg[/IMG][/url]
... will show the image and when clicked, will take you to the Google homepage.
The link to the image itself would obviously be the image you'd be using, so replace that. Also, you won't be using Google as a hyperlink either, so use the URL of the site you want in that specific area.