Alright, I was going to make a post for it, but I noticed Lewis already has done that. In any case, I'll fill information for this that he has not included.
Okay, other than installing/extracting the PCSX2 emulator, you will also need the Bios.
The Bios themselves are the software that the PS2 uses to play the games. If you've ever played with a PS2, you'll notice a 'browser' and things like that. This is exactly that software. The bios files also make things work, such as absolute emulation of the DualShock controller, sound emulation, things like that.
You can search Google for the Bios, best if you torrent it, because the Bios themselves are ILLEGAL. Yes. The PCSX2 Emulator is pretty much useles without them too.
You might also find speedhacks interesting. You can use this to make games run faster, but they actually slow down some other games. The idea is to remove things like fog and the like to improve the frame rate. This does not work for all games. It's more likely to work for popular games. The main reason your game runs slow will be processor speed. Your processor cannot match the PS2 processing speed, as you're also running a system resource heavy OS. You can achieve better playability by shutting down software you don't need. Your browser window, for example, can take up a lot of resources. Your RAM most likely has nothing to do with your slow frame rate.
I noticed this when PS2 versions of games run slower than the PC version itself. The answer is obvious. Notice how much you reduce the quality of your PC version? Your textures are either set to lowres, and your draw distance and clipping are low. Meanwhile, on the PS2 your graphics are all high by default, it's how the PS2 runs. Unfortunatly, I don't believe there are any speedhacks to reduce draw distance.
Okay, that's it from me. Not like anyone here has the love for Playstation to actually try it. Sigh.