2 Answers

Facebook does not have videos. Any videos posted to Facebook are from host sites like You tube. 

Unless you mean upload videos TO Facebook  then you just click video on your status bar and upload from your computer files or go to you tube and share the video to Facebook. There's a share button on the video. 

well very easy, just click the video exactly or its site address then you can see bottom corner there's an icon option share like. click the option icon then it shows download click on it and it shows small portion of another icon click save as then choose where do you want to save.

i tried it many times and i had many downloads on my computer from facebook like pictures and videos...