How to install a software on my linux box when I don't have root access (sudo)?

You can install youtube-dl through linuxbrew

Install linuxbrew:

ruby -e "$(curl -fsSL"

Add the line export PATH="$HOME/.linuxbrew/bin:$PATH" to your ~/.bashrc:

echo 'export PATH="$HOME/.linuxbrew/bin:$PATH"' >>~/.bashrc

Install youtube-dl:

brew install youtube-dl
youtube-dl -U

Just interpolate from the documentation.

With curl:

mkdir ~/bin
curl -L -o ~/bin/youtube-dl
chmod 0750 ~/bin/youtube-dl

Or with wget:

mkdir ~/bin
wget -O ~/bin/youtube-dl
chmod 0750 ~/bin/youtube-dl

Note its requirements.

It requires the Python interpreter (2.6, 2.7, or 3.2+).

If this a work server, know in advance whether you are permitted to install and stream.