Well first off you need to answer a few questions. I am guessing you are refering to FFXI, since playonline is only evident in that game(for ps2 anyway.)
1. Do you have a ps2 network adapter?
2. Is your DSL modem Ethernet(strange looking phone line?)
3. Do you have a router?Home network running?
If you answered yes to all of these, you should be able to just run an ethernet cord from the ps2 network adapter to your router.
If You have 1 and 2, but not 3, then you need to connect your ps2 directly to your modem and put any login information into the network adapter settings on the ps2.