Instructions
Set up an Internet connection on your PSP. Scroll to the left on the Cross Media Bar (XMB) until you hit the Settings tab. Scroll down to the bottom, and select "Network Settings." By default, your PSP Slim is in ad hoc mode, meaning that it can only connect to other PSPs within its vicinity. Select "Infrastructure Mode," and select your access point (source of wireless Internet). Continue through the options, customizing them as you see fit. Save the settings, then test the connection. After the test finishes, exit.
Scroll all the way to the right on the XMB until you get to the PlayStation Network (PSN) tab. If you already have a PSN account, scroll down to the PlayStation Store and select it. If not, scroll up to the "Sign Up for PlayStation Network" option. Select your desired PlayStation Network name and an e-mail address to attach it to. Complete the registration process, then access the PlayStation Store option under the PlayStation Network tab.
Explore the PlayStation Store&'s wide array of different PSP games available for download. Select one to buy and download. You will have to enter credit, debit or PSN card information (PSN cards are available for purchase in stores if you don&'t have a credit or debit card with which to purchase). After successfully paying for the game, select the option to begin downloading.
Keep an eye on your download. PSN will alert you when your download is finished. Look under the Game tab to install the game once it has completed downloading. The finished game will be installed on your PSP&'s memory stick and under your game library for as long as you have that memory stick in the PSP. If you decide you would like your game on a different memory stick, the game will be available for re-downloading on the PlayStation Store under the "Recently Downloaded" button.