Instructions
Navigate to the PlayStation Store from the PlayStation 3 home screen.
Search for the particular game(s) you would like to purchase and download. Double check your available hard disk space to make sure there is enough space to download the game. Most PlayStation 2 games take up significantly less space than PlayStation 3 games, but it never hurts to double check.
Select the game(s) you wish to purchase and enter your method of payment into the system to attach to your PlayStation ID account. You will not need to submit your payment information after the first time; you will have a quick-pay option available after the initial purchase.
Download the game(s) and wait for them to finish downloading.
Navigate to the game section and select the newly downloaded game(s) to play.