It's pretty easy, without installing any application on your PC:
1. In a computer, open your facebook and play the video you wish to download
2. Look at the address bar, change the "www" to "m". For ex: www.facebook.com/video.php?v=bla-bla-bla, becomes: m.facebook.com/video.php?v=bla-bla-bla then press enter (remember, only change the www don't change any other character)
3. The page will be viewed as if you open it in a mobile phone
4. Play the video again
5. Right click on the video and choose "save video as"
6. You can change the file name and save to your preferred folder
7. Wait, it is downloading.
8. The video is yours now. :)