Let me post two ways of downloading youtube videos which I know:

 

METHOD 1:Downloading without installing any package:

  • Go to video page and allow the video to get buffered fully.
  • Minimize the browser window.
  • Now go to the location /tmp.
  • To go to /tmp follow these steps:
    • open any drive.
    • click ctrl+L.
    • type /tmp and press enter.
  • U can see a video file stored that directory.
  • Copy that file and save in any other directory,for example in desktop.

METHOD 2:

This method needs to install a package called Clipgrab.

To install this package go to ubuntu software centre and type Clipgrab.Then click install.

You may also install this package by giving the following command in terminal:

sudo apt-get install clipgrab

Now copy the video url and paste it in the clipgrab package.After a while click grab this clip!.
Now your video gets downloaded and saved in the directory you specified..

Enjoy watching!!!!