Instructions
Plug your PSP's power cable into a wall outlet. You can only upgrade the firmware on your PSP if it is connected to a wall outlet.
Turn on your PSP.
Select "Settings."
Chose the "Network Update" option. If your PSP is not already connected to a wireless network, you will be asked to choose a connection at this time. Do so by highlighting the name and pressing "X".
Press "X" to download the PSP firmware upgrade. When the download is finished, press "X" again to install it. Once installed, this software will upgrade the functionality of all of the components in your PSP, including the Wi-Fi card.