Play the video, then Right Click -> Show video URL. See screenshot below.
Go to fb-down.net. Then paste the URL and Click 'Download', like the screenshot below
Click on "Download SD quality video" or "Download HD video" (if available) to start downloading the video.
Note 1: If the video opens up instead of downloading, then on Step 3 Right Click the link and "Save as..." to download the video.
Note 2: If you get an error, then check if the video is public and not private.