Instructions
Turn your Sony PSP on, put the Wi-Fi switch in the on position, navigate through the PSP menu and select "System Update."
Select "Update Via Internet" and select your home Wi-Fi connection from the list that appears.
Press the "X" button to agree to the terms of the software. This means you will not redistribute or modify the software in any way.
Press the "X" button to update the PSP software and wait until it reads "100%." Press the "X" button once more to reboot the PSP. You are now updated to the most recent software revision.