This depends entirely on what you intend to do....
You can backup a dvd movie on a DVD-R and not have to do anything and your PS2 will play it...
However, if you intend on backing up PS2 games, you will need a mod chip installed in your PS2 in order to play them.
You will need a dvd writer (to write DVD-R discs)
You will need a cd writer (to write cd-r discs)
And you will also need specific software: Primo DVD or RecordNow Max, Clone CD... (These are the ones used most for PS2 backups)
DVD Decrypter, Ifo Edit (For burning DVD movies) or DVD X Copy...
Any more questions, don't hesitate to ask...