Both phat and slim about 7 screws, you need a good quality size "0" cross head screwdriver. Just make sure you put the screws back in the same place (3 types) and the only other issue is DUST
It gets everywhere, even cleaning with mirror wipes still left a couple of small bits. Other than that, if its a phat you have to pull off the joystick top and unscrew it from the face plate.
All in all the easiest repair you can do to a PSP - I got mine from dealextreme (metalic red) not bad but make sure you put on a screen protector as the new face plate is not as tough as the original.