A more recent version of this guide can be found here.

OBS Studio shown running on Linux Mint 18.3.

Installing the amazing screen recording and streaming software from Open Broadcasting Software, OBS Studio, is easy on Linux Mint.

Run the following commands:

sudo apt install ffmpeg

sudo add-apt-repository ppa:obsproject/obs-studio

sudo apt-get update && sudo apt-get install obs-studio

Once you've completed those steps you can find OBS Studio in the Linux Mint main menu under the "Sound & Video" section.

This cross platform streaming and screen recording program is excellent and runs perfectly on Linux Mint and other Linux distributions.