To download a video you posted earlier
It is easy to download those videos from Facebook, which you had uploaded in the past. To do that you just have to:
1. Open Facebook and go to your Photos / Albums.
2. Select the video you want to download and open it.
3. Once you open the video, click the Options link under the video.
4. In Options link there are options like Download HD and Download SD.
5. Click on the required link depending on the quality of the video you want to download.
To download a video posted/shared by a friend
Unlike the ones uploaded by you, Facebook sadly doesn't allow you download those videos that are posted or shared by your friends. However, there are certain steps by which you can download or save any video uploaded on Facebook without any software:
1. Open Facebook and find the video you want to download.
2. Play it and select the link in the address bar.
3. Then change the URL in Address bar as follows- change "www" to "m" so that the initial part of the URL looks like https://m.facebook.com/...
4. Once you change it, press enter to open the mobile version of the page.
5. Once the mobile version of the page opens, click play and right click the video and then from the options select Save video as, Save target as or Save link as depending on the browser you are using.
6. Then choose where you want to save it.