Website Preview Graphic for WordPress Site

The accepted answer over on StackOverflow looks to be the best way to do this. You’ll want to get into your header.php file to make these changes.

https://stackoverflow.com/questions/6693499/how-can-i-set-a-website-image-that-will-show-as-preview-on-facebook

Now if the image should change from post to post, I would probably write something using JQUERY to change the value of the meta tag on the post.