If you're using Photobucket and you've got the pic uploaded on your account there all you have to do is just use the fourth link they give you and paste it where it says "signature" here on your profile in the profile settings:
Photobucket just makes things easier because it does the job for you by adding the [IMG] code brackets at the ends of the picture's link but the picture works the same if you use the method mentioned above by Ress & Thrill. Hope this helps you understand better