First, the obvious part of downloading the source from Meridian, it's the source link in his original post, I'll copy it here too:
https://github.com/MeridianOXC/OpenXcom/tree/oxce2.9-plus-protoEither download or make a git clone, just get all the source files in a directory you can easily find with the terminal.
Next come all the required libraries, listed on
https://ufopaedia.org at:
https://www.ufopaedia.org/index.php/Installing_(OpenXcom) under the instructions for Unix-like systems. We need all the dev versions, so I installed them with the command
sudo apt-get install libsdl1.2-dev libsdl-mixer1.2-dev libsdl-gfx1.2-dev libsdl-image1.2-dev libyaml-cpp-dev libboost-dev
Note the addition of libboost-dev - I don't remember quite why I needed it, I think it popped up as an error that it was required during my first try.
Finally, navigate in your terminal to the src folder from Meridian's files and make using the Makefile.simple that he provided:
make -f Makefile.simple
After a few minutes, you should have a binary that you can use! I then moved it to the Piratez directory, the same location that Dioxine puts the .exe file for Windows. Make sure it's set as executable, and you can either run it from a terminal or just double-click from a file browser.
Edit: If you're having trouble finding the executable after compiling, it was in the bin/ subfolder for me.