Right, if you have old ps2 (the Brick) you can purchase a network card. these are hard to get hold of as they don't make them any more.
Next is an internet connection broadband must a Ethernet connector (a network lead). USB connection will not work as far as I know.
plug it all in. Insert disk that came with the network card, follow the instruction and hey presto done.
The only fault is that the connection is nothing like xbox live.
I currently have my ps2 online for NFSU2.
if you have a slimline then it's different, it has an inbuilt network plug in and go I assume as I have not got one of them.
Hope this helps
Cheers