Instructions
Look in your external hard drive manual to make sure the hard drive uses the FAT32 file system. Many external hard drives come pre-configured using the FAT32 file system, but some do not. If yours does not, you'll need to download a formatting program and format the disk to the FAT32 file system. Programs, such as Easeus Partition Master, SwissKnife and Partition Wizard allow you to format the hard drive so that it's compatible with the PlayStation 3.
Connect the external hard drive to your PlayStation 3 via the provided USB cable. Turn on the PlayStation 3 console and sign into your account.
Back up your entire system by navigating to "Settings" on the main PlayStation 3 screen. Scroll down to "Backup utility." Press "X" on your controller. Click "Backup" and select "USB mass storage" as the device to use. This will back up everything on your PlayStation 3 to your external hard drive. If you'd rather copy individual files, you can do that, too.
Press left or right on the controller's analog stick on the main PS3 screen to navigate to the different files on your PlayStation 3, such as music, video and photos. Press down to choose which file you would like to copy. Press the "Triangle" button on your controller and select the "Copy" option. Choose the "USB mass storage" as the device to use.
Press the "Triangle" button to transfer files from your external hard drive to your PlayStation 3 system. For example, if you want to transfer over music files, you can scroll over to "Music" on the main PlayStation 3 screen and press the "Triangle" button. From there, you can select the file you wish to transfer over.