First, you have to have an image hosted. One service I like to use is tinypic.com
then in your signature, you put the following:
[img]http://www.websitename.com/picturelink.jpg[/img]
Keep in mind there are size restrictions. It may auto-resize the image for you but if it's distorted then you'll need to edit it yourself. I think 80X80 pixels is the maximum picture size.
For example, if I were to put the following in:
[img]http://www.vacwarbirds.org/AirplaneGallery/images/DSC0951-C47-TICO-Belle.jpg[/img]
then it would show that image: