You already have those links.
The first post has a link to the mod and to GZDoom.
wildweasel gave you a link to FreeDoom (you'll need Phase 1 I think).
You've also been given links for instructions on how to set up ZDoom.
Basically, it should just come down to installing everything by unzipping it all into the same directory, making sure that the FreeDoom WAD has been named doom.wad (rename freedoom1.wad to doom.wad) then running one of the bat files that come with the mod.
When you have installed all the files it should look something like this:
Then double click FNAF-Host.bat
Remember to set your preferences, screen resolution, mouse look, key binds etc, then you should be good to go.