The easiest way is to use a FF extension (add-on). I have not found a
satisfactory one for Chrome/ Chromium yet. The FF one that I like is called
DownloadHelper and I have used it successfully for many years. It will not
work (none will) if the video is not cached. Some videos will do this to
prevent copying. You can save the video in various qualities and it can
capture just about every format from flv to avi and mp4. It can convert
from one format to another as well.

Install Video DownloadHelper in Firefox. Tools/Add-ons. It's version 4.9.8, its
icon is three small circles, yellow red and purple.

Chrome or chromium has an excellent extension addon youtube downloader it
adds a download button directly beneath the video on the youtube page and
gives you the option of downloading up to 1080p all the way down to audio
only mp3