Ps2 online with mini ps2?

I've had a big ps2 and a mini one for a few years, but didn't understand what it meant to be pre-setup with online as the mini version claims to be. My friend says he takes his ethernet cord and plugs it into the ps2 to get online but although this got me into it, it wouldnt connect to play with other people. Should I get an adapter and what do they cost/where would i get one?

I know ps2 is obsolete but I'm not getting a ps3 due to the lack of games and price and the popularity of ps2. Madden 09 will probably still come out for ps2 anyway. Thanks.