Replacing the battery on the PSP is highly recommended as the batteries often no longer carry charge and can expand, breaking the plastic shell of the PSP.
1000, 2000 and 3000 Models
Replacing the battery on the X000 Models is simple. There should be a button on the back of the PSP for the 1000 models, and on the side for the 2000 and 3000 models. Press the button and push outwards and the panel should come off. Remove the battery and insert the replacement.
Remove the back 4 screws and the top 2 screws to remove the back panel. Remove the warranty sticker if it is present and remove the battery from the PSP, carefully avoiding bending the flex cable. Place the new battery in the PSP and reassemble.
Open the UMD door and press a side of the metal tray and lift it towards the UMD door. Repeat with the opposite side of the metal tray and gently wiggle until the tray is separated from the PSP. Now gently pull the UMD door out from the PSP, starting from one side and making your way to the other side. Once the door is removed, remove the sticker above the Sony logo and then remove the screw. Lift the battery out of the PSP and carefully lift the cable out the PSP. Replace the battery and reassemble, being extra careful with the UMD door.