Welcome to the forum mate
Take some time to read up on the 'sticky' posts at the top of the sub-forum. The 'sticky' on
Backup Procedures gives tutorials for the best programs.
To start with PS2 games are either CD or DVD format. To backup a CD based game to CD-R, you need a CD-writer and either CloneCD, CDRWin, Alcohol 120% or Nero (there are some others). To backup a DVD based game to DVD-R/DVD+R, you need a DVD-writer and either RecordNow Max, PrimoDVD, Alcohol 120% or Nero (there are some others).
You will also need some kind of mod-chip device in your PS2 console to play these backed up games.
Hope that this gets you started.
Any problems/further questions post back