Instructions
Turn on your PS3. Log in to your PlayStation account. If your console requires a firmware update, you will need to complete this process before you can log in.
Navigate through the cross media bar (XMB) until you reach the "PlayStation Network" tab and select the PlayStation Store icon. The PlayStation Store takes a few seconds to fully load up.
Select the "Downloadable Games" button on the main screen of the PlayStation Store, and then click on the "View All A-Z" button on the next screen.
Choose which PS2 game you would like to download from the available choices. Game information --- developer, publisher, year of release, number of players --- will be provided in the information panel on the left side of the screen.
Click the icon of your desired PS2 game to pull up the main information screen. Confirm the purchase when prompted by clicking the "Confirm Purchase" button. You can wait for the game to download, or you can choose to download the game in the background by selecting the "Perform in Background" button.
Find your downloaded PS2 game by exiting the PlayStation Store. Press the "O" button several times to back all the way out and navigate the XMB to the "Games" tab. Click on the icon of your downloaded PS2 game to complete any necessary installation and updating procedures. Your downloaded PS2 game is now ready to play.