Here are instructions on how to install OBS Studio on Linux Mint 19. These instructions will probably work on earlier and later version of Linux Mint and Ubuntu.

The following are the commands to run in a terminal:

sudo apt install ffmpeg
sudo add-apt-repository ppa:obsproject/obs-studio
sudo apt update
sudo apt install obs-studio

Once it's installed after completing those commands you can find OBS Studio in the Linux Mint menu under the "Sound & Video" category. 

The video on this page explains everything explained above.