Is your PSP not fully charging? The problem could be the PSP's battery and not the charger, in which case your best bet is to contact Sony for support and options. If you are sure that the problem is with the charger, however, you can either buy a new charger or try to make the repairs yourself.
If you are certain that there is no voltage coming from the charger, you can take apart the charger casing and check the connections of the AC plug connector. If the plug was somehow bent, you can fix the broken solder and get the voltage flowing again.
You can also replace the plug itself, if you are capable of soldering. If you are not capable of doing such repairs, contact Sony or try returning the charger.
Call Sony customer service and explain the problem with your charger. If you have a receipt, they may send you a new one for free. While you are waiting for your new charger, you can charge your PSP with the USB connector.
If you have exhausted your other options, purchase a new charger, making sure to keep the receipt. If the problem persists, the problem is most likely with your PSP. Contact Sony customer service.
Never use a generic AC adapter to charge your PSP, as this could damage the battery system of your PSP. Your best choice is to charge your PSP by connecting to a computer with the USB connector.
Make sure that the charger has proper voltage flow. Make sure that the problem isn't with the PSP itself. Always check your warranty and have a receipt on hand, if possible.
Do not use a generic battery charger.