If it has an LED back light, use the PWM from the PIC (look at the data sheet on how to use) and a transistor like a 2n3904... put the PWM on the base of the transistor (through a small resistor) with the transistor emitter to ground. Put the LED back light form V+(anode) to the collector (cathode) with a series resistor so you don't burn the LED.... that is the most simple way...
Vary the brightness by changing the duty cycle of the PWM (also explained in the data sheet)