It depends on which version of the program you have.
But, if you're using version 11 or 12, use Publish & Share/Computer/AVCHD with the YouTube HD preset to output your video. Then load it to Facebook as you would any photo or video.
As asked by SG, what version of Premiere Elements are you using? What computer operating system is your Premiere Elements running on? And, is your edited video SD or HD?
Do you have the project file for the "edited video clip". If so, you might explore the upload of the Timeline content to Facebook using the Premiere Elements 10, 11, and 12 feature for that purpose...
For Premiere Elements 10, Share/Online/Facebook
For Premiere Elements 11, Publish+Share/Online/Facebook
For Premiere Elements 12, Publish+Share/Social Websites/Facebook
Did you try one of those and had a problem doing so?
Looking forward to your follow up.
If you want to upload to your own timeline you can use the Share option within Elements.
If you want to upload on a friend timeline you will have to export the movie to hdd first, then upload via Facebook.