Instructions
Browse through the PSP's XcrossMediaBar menu until you get to the PlayStation Network Store icon on the far right of the menu and select it with the "X" button.
Select the "Games" section of the store's homepage to be shown the list of available games that can be installed onto the PSP's memory stick.
Select a game that you want to download, and select the "Add to cart" button on the top right of the screen.
Select "Checkout" and enter in your payment information (credit card). Select "Yes" to verify your purchase and the game will automatically be downloaded and installed onto the PSP memory stick.
Press the "O" button on the PSP game pad until you are returned to the PSP menu. Select the newly installed game in the PSP menu's game section to play it.