Since Facebook doesn’t allow you to upload directly your GIFs in a post (you can directly upload GIFs to Facebook Messenger only) you will have to host your GIF somewhere before posting it on Facebook.
We recommend Giphy for this purpose. Here are the steps below.
1. Go to http://giphy.com/upload
2. Upload your GIF and copy the GIF link (ends in .gif)
3. Paste your GIF link in Facebook!
For more information about sharing GIFs on Facebook please refer to this great article on Giphy.