Instructions
Start the PSP. Scroll to the "Settings" tab with the d-pad. Highlight "Network Update" and press the "X" button.
Select connection. Highlight the name of your personal wireless connection. Press the "X" button.
Wait for the PSP to scan the current firmware. If an update is available, it will download automatically. This will roughly take about 10 minutes, depending on connection speed. If an update is unavailable, the PSP will state, "You Have the Current Version."
Update after download. Scroll to the "Game" tab. Then go to the "Memory Stick" icon and press the "X" button. Then, highlight "PSP Update Version X.XX" and push the "X" button again. Your PSP firmware will update.