From what I remember with my old online setup (wired), you need:
-High speed internet (cable or DSL)
-A router (I think you might have to open/forward ports too, might depend on the game)
-I used Linksys' USB ethernet adapter at the time (This one: http://tinyurl.com/8sfap), but I don't know what people use now. You plug it into your PS2's USB port, and a network cable into your router (basically making your PS2 another "computer" on your network).
I don't know if wireless is available, but this is what I used back when I played Tony Hawk 3 and 4 online a lot. Things might have changed a bit though since then.
[quote name='rain24']I have the big ps2 one.[/QUOTE]
A network adapter. Just go to EB games and get it used for $17. Make sure it comes with the setup disc. Then, you can plug it into your modem, hub or router.