Firefox is the best web browser out there (in my opinion) and they're lots of great extensions which will help you with this.
Download this:
Firefox
(If you don't have it already)
Download and install this extension, this may require you to restart Firefox. Once installed they'll be a small symbol on the bottom right-hand corner of Firefox. Click that on a page that you want to get the video from. You'll have the option to either download it or it'll give you the URL from where its located.
Once you have downloaded (or found the URL for) the video you can host it elsewhere if you feel like doing so or you can put it in your profile for all to see.
Note:
Not all videos or websites work.
If you are more experienced with computers check out DownThemAll. It has many more features which will make things easier for you if you know what you're doing.
