To add a background video, go to the theme options panel (Appearance → Theme Options) then Background → Video. At the Background video URL setting, enter a URL to a YouTube or Vimeo video.
So that the video can be scaled properly in different browser window sizes, you should enter the dimensions of the video. If you went with the Vimeo video, this information will be fetched automatically after you enter the URL. For YouTube you will need to find the dimensions manually: follow the link in the option description for instructions.