All you need is a video caption card and a the right wires. Though I believe that they have discontinued the model I am familiar with using, ATI made some called the ATI TV Wonder, and TV Wonder VE, which work quiet well for cheap. It is simply another card to plug into your computer (like your graphics card, sound card, etc) It will have inputs on the back of it. In the case of the TV Wonder VE it has a rca video jack and a stereo phone jack for the audio. The PS2 video out would hook directly, and then you would have a small jumper from the audio jack to the soundcard, and then an adapter from the soundcard to the 2 PS2 audio lines. This is just one example, and there are many different manufactures out there that make cards like this. Do a search online for video capture cards, or even TV Tuner cards (just make sure they have the video capture option). If you have the money, most of the newer more "top-of-the-line" video cards have the capture built in. Just make sure that you are aware of the type of connections it uses, and that you have the proper wiring to hook it all up.

Yes, there is only a direct connection for the yellow (video) line. If you picked up the TV Wonder (VE), it should have come with a small stereo jumper. You connect the stereo jumper (it looks like the end of a set of headphones) to the capture card output, and then connect the other end to your sound card auxillery input. This way the sound captured will have the ability to be played. Then you will need to purchase a "stereo to RCA" splitter. Its a small adapter that will have 1 male stereo jack (like on the jumper) and 2 female RCA jacks (the red and white). Plug the red and white RCA jacks into the splitter, then plug the stereo jack into the capture card audio input. Now you have sound. =) On a side note, I have done this before and its not really worth much. The games will not look as good on the computer monitor for one. Television resolution is much lower than what a monitor runs at. Not to mention the capture card will cause quite a bit of lag in controlling the game. You lose about a second between when you enter a command (ie. pushing up on the controller) before you see it on the screen. This can make any game extremely hard, and some even impossible. Cheers! -SC

excellent answer, but i just wanna give a little tib bit of info, i've heard that playing the ps2 through the pc causes video lag. not sure if this is true, just a rumor.....

Some TV Capture cards accept the yellow Composite Video Jack, I tried this and got about 3 - 5 seconds video lag making it impossible to play.