Instructions
Turn on your PS3 but do not load a game. The main menu will come up. Click "Right" on the direction pad twice to access the PlayStation Store. You'll automatically log in if you already have a PlayStation Store account. If not, register for one first.
Click on "Games" and then browse through your options until you find the DLC you want. Some games have multiple DLC packages. Browse through them until you find the one you want. Once you've selected the DLC, look to see if it costs money. If so, add cash to your wallet.
Return to the PS3 main menu, select "Account Management," and then click "Transaction Management." Enter your credit card information and the amount you want to deposit into your wallet. Once the transaction is complete, you'll be able to use the money in your PlayStation Store wallet.
Click on the "Download" button. If the DLC costs money, you'll be prompted to confirm your purchase. Click "OK" and the download will being automatically. A status bar on the bottom of the screen shows the percent completion of the download. Once it's done, you'll be able to install and play the DLC.