You just have to have a game that’s compatible, and a router. Linksys makes pretty good quality cheap ones, wireless or wired.
Then depending on your setup and preferences, you can get a wireless gaming adapter (There’s also a more expensive one on amazon, I’m not sure of your budget.) to hook your system up over wi-fi. This way can be quite laggy, though, and if you’re new to online gaming you might not understand the magnitute of frustration that your screen being choppy and you trying to shoot someone and them not even knowing you exist can be.
The only way I would recommend wireless is if you have a really stellar wi-fi network already, and your system is either really close (So you get awesome signal), or so far away from your router that running an ethernet cable to it would be impossible.
Leading to option two; a wired ethernet cable. This is the really simple meathod. You still need a router, but not a wireless one, and you just plug you system into it with the ethernet cable. Keep in mind that the shorter the cable is, the better connection you have. You can still suffer lag even with ethernet.
Then it’s a matter of telling your system to recognize your network. I believe the game should give you the chance to do this when you log on. Go to multiplayer, and online. If not, then check around the menu (As in, turn the system on without a game in it, and see if there’s a place there to set up a network.) My ps2 isn’t plugged in since I have a ps3 now, or I would really check it out for you. Let me know how it goes though. I may have it in m to dust it off :)