Facebook doesn't officially support GIFs, but that doesn't mean that others aren't going to try and make it so.
The first thing you need to do is to head over to GIF search engine Giphy
to pick your favourite GIFs. Then either copy+paste the URL of the page for the GIF you've selected, or embed straight to Facebook from that page from the portion where it says "share GIF."
Once its up, you should see a play button on the embed that will let the GIF play on a loop. It might take a little while to load, but we can tell you that it's well worth the wait.