The problem our client was having was that, whenever a page of theirs was shared on Facebook, the default picture (or the first option) was the cover of a book. They wanted their logo to show up instead.
Even if you are not having the same problem of unrelated images showing up when sharing pages on Facebook, it makes sense to control your Facebook presence by regulating what images appear when people share your links. It looks better, and it creates a unified brand for your organization. Also, it's really easy!
Here's what we did when we set this up for the MomsRising blog:
We grabbed the MomsRising logo from their Facebook page and gave it a nice shadow and border in Photoshop. We also made it 100px square, so it would fit nicely in a Facebook post.
Then, we added this code to the header region of our page by placing it inside header.php:
<meta property="og:image" content="http://example.com/image.jpg"/>
We uploaded the image and the new header.php via FTP, and voila! Whenever someone shares a link to the MomsRising blog, the default image is their nice logo.
NOTE: There seems to be some issue with Facebook's caching system, which just means that it will work almost all of the time instantly, but it will take a little while for it to work all of the time.