Okay, the information given was still not complete here but helped us a lot when me and my friend set out to get a ps2 to ps2 game going using an X-Over cable. (cross over)
The above information is right, about changing DHCP to NO and setting the ips to something like 192.168.0.1 and 192.168.0.2
Howoever, this still does not work without some tinkering.
One PS2 has to be set to host in the Lan Options in the options menu. Leave monitors at zero (unlike previous posts indicate) Also set the players to two.
Make sure that in your network options in the options menu that auto connect is not on.
For it to work, the person JOINING the game, not hosting, must hit connect on the connection screen before the host does, by about two seconds. If you don't do this right, and you don't have freshly booted PS2's, it probably wont work. If you have any problems connecting at all, you need to reboot them again and start over.
Also make sure that your lan configs are getting saved, as their is no autosave outside of Gran Turismo mode. You can do this by going to the main menu and hitting save game.
We had some problems still, we would get all the way to loading up the race itself and it would freeze, but started over and everything was fine, and played about 20 times consecutively with no problems. You do not need to recreate a lan session after every race, just to clarify that.
Any cars that you use in lan mode must be "added to your favorites" in arcade mode. There are no garage cars available, and no replay saves available. A few select cars will not work even if you have them added to favorites for whatever reason. For instance, trying to use the Prowler in Lan mode gives the error "Cannot be used in 2p battle mode"
Its pretty dry, and not real feature rich, but you can still have some good races. We experienced no stuttering and no fps drops, everything was silky smooth, of course after spending the 3 hours on trying to figure out the sequence to get it to work.
Hope this helps some of you that are still having problems.
EDIT: your track registrys do not need to be identical, if the host selects a track that is not in your registry, the other ps2 will automaticly switch to it. Also, replays are viewable on both tv's imediately after the race, and everything is synced, so if one person exits the replay, you both exit. Same thing with pause during race. I will add whatever else I can think of.
EDIT #2: To answer the above post, the number of players are configured in the lan options menu, but I as well, cannot find a place to change the number of laps, after searching for a while. Please post if you have any solution to this