Google for "uLaunchELF" and read about it since discussing how it works will be lengthly.
With this program and other similar file management apps for PS2, you can transfer game saves from your PS2 memory card to a compatible USB flash drive (most flash drives are compatible anyway particularly those from CDR King) and then transfer from flash drive to PC.

You can make a PS2 CD or DVD with uLaunchELF on it or you can boot it directly from memory card or from USB flash drives using any methods found on the net. Google for it - don't be lazy.

Now there are other ways like some cheat code disks which use usb flash drives for updates or game save transfers but as pointed out by many PS2 gamers, your save games usually come out corrupted.

Lesson learned? -> Google is your best friend