hey ashley,
easyblog already has a facebook like and share feature built-in as you can see here: http://screencast.com/t/Zse2Ph8DbF

in fact it offers 3 ways right now out of the box which is native buttons (at the bottom in this pic) and "add this" / "share this" service integration (at the top).

hope that helps and have a nice day

When looking at our Settings>Social Integrations, I'm not seeing a "Facebook Share" feature that I'm able to enable. Can you point me in the right direction of this? As you can see, our blog (https://www.tdecu.org/abouttdecu/blog/latest.html), does not have this feature already built-in. I appreciate your help!

sure, you're actually already at the right place.
when you're at easyblog -> settings -> social integrations you should see a tab called "facebook likes". there you can enable both the like and the share (send) button. the screen should look like this: http://screencast.com/t/BaphmnW1C

if you have enabled the settings on this page and you still don't see facebook in the frontend please provide us with your site and ftp access so that we can check this directly at your end. hope that helps and have a nice day