Instructions
Turn on your Sony PS3 and select the PSN Store icon from the main menu. Select "Add-ons" from the PSN Store main menu.
Select "Disc Based Add-ons" from the menu that appears. Browse through the list of available add-ons. Select "PS2 System Data" from the list. This is a free add-on and allows you to play your PS2 titles on the PS3.
Select "Add to Cart" and "Checkout" from the menu that appears. Since it is a free download, you do not need to input any payment information. The PS2 system data will automatically download and install onto your PS3.
Exit out of the PSN Store and insert your PS2 disk into the PS3. Select it from the PS3 game menu and it will boot up.