Instructions
Place your Sony PSP's memory stick inside its memory slot. You cannot update a PSP's firmware via the Internet unless the memory stick is inserted.
Turn on your PSP. Select the "System" main menu option.
Select "System Update." From this screen, choose "Update Via Internet."
Select the name of the wireless connection you want to use to update your Sony PSP. Pick a connection that is stable; if you're currently moving away from a connection or have a weak signal, choose another one because a weak connection can disrupt the download of the update.
Press the PSP's "X" button. This will download and install the latest firmware update.