How do i connect my PS2 to the internet?

I have the 2nd gen PS2(thin version). i have road runner high speed/ wireless. the router is 2 floors bellow the PS2. there is a computer in the room next to the PS2 which is hoked up with a wireless USB adaptor. can i take the USB adaptor from the computer and plug it into the PS2 USB? or do i need a earthnet cable? if i have to buy a cable how does it give me internet access. i know 1 end would go into the PS2 but wht does the other end plug into.