You have to buy a converter. Before you run a game, you have to load a cd for the converter each time. Don't know of any other way. Well, I do, but it was less than favorable. I bought a vga switch. The only thing I hooked up to it was the PS2. On my 19" monitor, the game took less 50% of the screen. Also, it was doubled. Like I was looking a two seperate images. It looked like steaming poo. It also reset my PS2, and then the PS2 wouldn't power on. Scared the crap out of me. Well I finally hooked it back up to a TV eventually and it worked fine.
I read on, I think it was liksang.com. That the PS2 doesn't nativley support VGA, that you have to load code into it, hence the CD. Which is a shame because my dreamcast looks awsome on the PC monitor.
Hope this helps. If you find an alternative, let me know (PM me even) because it would be great to find a way.