Instructions
Turn on the PS3 system. Wait for the main menu to load. Choose the "PlayStation Store" option.
Select the "Browse Games" option. A list of PS2 games, among others, will display.
Highlight the PS2 game that you want to download and press the "X" button on your PS3 controller. Select "Confirm Download" to initiate the download. Ensure that you have sufficient funds in your PlayStation account to download the game. If you do not, you can use either a debit or credit card to download the PS2 game.
Allow the download to complete. After you have your PS2 game, exit the PlayStation Store. Select the "Games" section in the PS3 main menu. The downloaded PS2 game is contained in this section. Select the game, press "X" on your controller and the PS2 game will load.