If you're using the US or Japanese releases of Version 2 of PSO (or the Japanese original release), then you'll need to go download/burn the Sylverant PSO Patcher (which is what Bob Dobbs was referring to). Even if you're using the European release of Version 2, I'd still recommend grabbing it as it has some bugfixes for the game included with it. You might also see it listed as "BlueCrab's PSO Patcher" or something similar (or even just the "PSO Patcher"). There are plenty of different places you can get it from.
Basically, you'll want to boot your Dreamcast up with that disc when you want to play online. It'll ask you to swap in your GD-ROM of PSO and once you do so it'll let you boot it in a way that will make it so that it'll connect to Sylverant instead of trying to connect to the now non-existent official servers. You will have to do this every time you want to play online, as the patches it makes are only done in the RAM of the console and don't survive reboots.