Since Tirion's mod works off of RetroArch, I figured I'd write a short tutorial on how to get it set up. Fortunately, the RetroArch developers are already pretty good at that:
Their webpage has downloads and installation videos and instructions for just about every system you can imagine.
RetroArch itself is not an emulator but instead runs off plugins called "cores". Once you start RetroArch, you'll need to go from the Main Menu to "Online Updater" -> "Core Updater", then find the PlayStation cores. There are two: "Sony - PlayStation (Beetle PSX HW)" and "Sony - PlayStation (Beetle PSX)". The only difference, I believe, is that HW offers more features. Select and update one of those (or both!).
To get
Chrono Cross (or any PSX game) to work, however, I believe you also need some of the PSX's bios files. Specifically, SCPH 5500, 5501, and 5502. Find these online and toss them into RetroArch's "system" folder. You can then Import Content from inside RetroArch to find your game.
I'm not quite sure how to use
Tirion's mod that will enable us to play
Cross in upscaled textures, so I'll give the floor to them.
All other discussions specifically related to RetroArch and this project can be had here.