Instructions
Turn on the PSP. It can be powered with either the battery or the AC adapter.
At the main menu, navigate to "Settings/System Settings" using the directional keys.
Press "X" to enter into the system settings menu. When all of the system information is displayed, rotate the analog stick in a circular motion. This tells the PSP the full range of motion of the analog stick and will fix any "drifting" or "sticking" issues you may have with the analog stick.
Turn off the PSP and power it back on. The analog stick should be functioning at full capacity.