What are instructions on how to download videos from YouTube?

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youtube-dl

Installation from official site:

sudo curl -L https://yt-dl.org/downloads/latest/youtube-dl -o /usr/local/bin/youtube-dl
sudo chmod a+rx /usr/local/bin/youtube-dl

It's also on Ubuntu repos but you will often need to keep it up-to-date with sudo youtube-dl -U

Installation and ugrade from pip (/):

sudo -H pip install --upgrade youtube-dl

Usage:

youtube-dl YouTube-(or-other-website)-video-link

So it will download the video.

You can also take a look at this for very in-depth documentation on how to use it.

youtube-dl is a great tool for downloading YouTube videos. Install with:

sudo curl -L https://yt-dl.org/downloads/latest/youtube-dl -o /usr/local/bin/youtube-dl
sudo chmod a+rx /usr/local/bin/youtube-dl

Or with pip (python3-pip):

sudo -H pip install --upgrade youtube-dl

Or from Ubuntu's repo (older version)

sudo apt-get install youtube-dl

then use it this way:

youtube-dl [VIDEO_LINK]

For learning more about advance options, run

man youtube-dl

Or check out the documentation.

Original answer

For Firefox users:

You can install the Video DownloadHelper addon in Firefox and download any embedded object, including YouTube videos.

Minitube

Minitube is a YouTube desktop application. With it you can watch YouTube videos in a new way: you type a keyword, Minitube gives you an endless video stream. Minitube is not about cloning the original YouTube web interface, it aims to create a new TV-like experience.

It does not require Flash Player. From this application you can watch and download videos.

Browser addon:
http://www.clipconverter.cc/addon/

Other sites that can be used:

http://www.clipconverter.cc/
http://keepvid.com/
http://www.listentoyoutube.com/

And this software is also great:

http://www.4kdownload.com/

I think that the simplest way to download a video from YouTube, without installing any plugin or software, is with savefrom.net. And here is the video demonstrating How to download YouTube videos using the ss trick. Let's say you want to download the below video:

On your address bar, add ss in front of youtube.com and hit Enter ↵.

Now you will be redirected to savefrom.net. On your right, click on the video quality you want to download.