Updated 2013/07/29: Facebook has changed where to find the settings described below. Updated the link to display the current information from Facebook’s Help Center.
If you want to share screenshots via Facebook, there is an easy way to do so with Greenshot: simply use the so-called post-by-email address Facebook has set up for you.
In case you do not know your post-by-email address, you can find it out very easy, Facebook’s Help Center entry tells you how to do it.
Once you know it, the rest is quite easy: Take a screenshot with Greenshot and use the E-Mail feature with your upload email address to upload it to Facebook. If you want to add a description, you can do so by typing it into the E-Mail’s subject. That’s it :)
P.S.: Of course we are aware that Facebook offers interfaces to upload images directly from a desktop application. But as there is no Facebook Plugin for Greenshot yet, uploading it via email is currently the easiest solution to share your screenshots on Facebook.