Instructions
Unlatch the batter cover on the back of the PSP and remove the battery.
Use a Phillips screwdriver to unscrew the two black screws found inside the battery bay. You will have to remove the warranty sticker in order to reach one of the screws. Removing this sticker will void the console's warranty, so if you are still covered you should send it in to Sony for repairs.
Unscrew the two screws located on the opposite side of the battery bay on the back of the console.
Unscrew the silver screw located on the bottom of the PSP. You will find this screw next to the systems barcode sticker.
Remove the thumb pad on the front of the PSP. This piece will snap off of the device and needs to be removed in order to remove the faceplate.
Lift the faceplate off of the front of the console. You will find the analog device attached to the underside of the faceplate.
Unscrew the two screws that secure the joystick pad to the back of the faceplate.
Remove the top cover of the joystick pad. You will find two plates with perpendicular lines etched in the middle. These provide the up/down and left/right movements of the joystick. If your joystick is broken, more than likely it will have come loose from one of these slots. Slide the joystick back into place and replace the joystick pad back onto the faceplate.
Reassemble your PSP and test the joystick to ensure its functionality.