backing up PS2 games is very easy. All you need is DVDdecypter. Simply use the ISO read function to transfer the game onto your hard disk. Then ISO write to burn the game. A few games are larger than a single layer blank dvd (Gran Turismo 4 and others). A more complex method is necessary for these games but I'm not sure what exactly.
The modchips/swap disks allow one to play the backups. Unless you plan on running emulators or Imported games, I would suggest the swap disks as they are much easier to install. The modchips require soldering tiny contact points which I personally found quite impossible. The modchips can however, be installed by professionals at a very resonable price ($25-$40 usd + shipping)
For more info on these check out mod-chip.com