Ok there are two motherboards for xbox360 controllers. The older one is the Matrix style, which will be difficult to accomplish this mod with, and the newer one is CG, which will be perfect for this mod.
CG means common ground, so when the buttons are pressed, it makes a connection to ground. So simply put you just need to hook you Positive side of your leds to the +3V connection then connect the negative side to the part of the button pads that gets connected to ground. When the button is pressed it connects the LED to ground and makes a circuit. (remember to use resistors with your LEDs)