Make sure the activity you want to share is not locked. One of the icons to the left of your activity name should show an open padlock. Then click the share icon, then the facebook icon.
Note: If you're using IE8 or IE9, the page needs to be displayed in "compatibility view" for the share icons to function. Click the icon to the right of the address bar, or go to tools campatibility view settings and add "garmin.com" to the list.