For this instructable's purposes I will be using Call of Duty: Modern Warfare 2 on the PlayStation3, generated screenshots are not mine.
Step 1: In Theory ...
If you are unfamiliar with different video signals see the images below. I do not address HDMI or DVI output in this because they require more hardware.
The PlayStation (or Xbox or whatever console) generates a signal that it sends through its AV output. Now how do we get this composite, component, or S-Video signal onto the computer. How do we make the console look like a camcorder to the computer? It would be easy if the PS3 or Xbox had a firewire output, like camcorders, but they dont. So we need a video card that can take a composite, component or S-Video signal and send it into the computer on firewire.