Turn off your PSP and remove the battery cover from the side of the back of the unit. Then lift out the battery.
Use your Phillips screwdriver to remove the four screws in the corners of the battery compartment, the two screws on the top and bottom of the side of the PSP, and the single screw located on the very bottom of the unit.
Pry the faceplate gently off of the unit with your fingers. Then use the tip of your screwdriver to pop the rectangular button bar just under the LCD screen off of the unit from where it connects to back panel.
Use the tip of your screwdriver to pop the four tabs on each corner of the LCD screen. Then lift the screen up and unplug the thick ribbon cable from the back of it. Set the screen aside.
Remove all screws from the LCD panel covering the rest of the unit. Then remove the panel to expose the motherboard and plastic triggers underneath.
Remove the left and right plastic triggers from the body of your PSP with your fingers.
Find the yellow plastic tube on the right side of the PSP, just under the circuit board. Above that is the positive conductor which is identified by two small holes right next to one another.
Take three 3/4 inch lengths of circuit wire (available from any electronics store) and solder the end of one of the wires to the end of a 10 OHM electrical resistor (also available from any electronics store). Solder the other end to the positive conductor on the motherboard.
Solder the ends of your other two lengths of wire to the bottom of the two small LED lights (available from any electronics store) and then solder the other ends to the resistor. Add a small patch of electrical tape over the resistor to secure it to the board.
Fit the LED lights in the small open spaces in the side of the plastic triggers and place a drop or two of hobby glue in the space to secure the lights. Then replace the triggers. After that follow the PSP disassembly steps in reverse to put your PSP back together. At this point the triggers will light up whenever you are playing the PSP.