Fastest way is to just put some HTML code that people can paste in their page. There's no need for buttons or form, just a simple link.
Something on the lines of:
<a href="http://www.yoursite.com/">
<img src="http://www.yoursite.com/yourlogo.jpg" alt="yoursite.com logo" title="Visit yoursite.com!" />
</a>
You'll probably want to add a couple of style tags (e.g to avoid borders around the image etc)
Also, it would be easy on your site to have a little JS that changes the code above so that people can personalize it (point to different images, different sizes etc etc)