Unfortunately you can't use Teamspeak on PS2.
Cray posted the link to it, it's a program that runs on the background in your computer. You need an IP address for a chat room or purchase your own.
I BS a lot with Sonofosiris, we even do singing contests. I'm just a guest in the room, so no idea if anyone can just join us or how it works.
I play PS2 but use Teamspeak on my husband's computer when he is not home.
Feel free to ask Sonofosiris about it, or even /slap him. It's ok, I promise. =P