> I'm using the PIC18F4520.

Joe, this example is for the 16F877 but PWM set-up is very similar
for the 18F4520

http://www.piclist.com/techref/microchip/16F877/pwm.htm

If you read the PWM section in the datasheet you'll see

As for the circuit, use the PWM to control an N-ch FET placed between
the cathode (k) of the LED and ground. From memory the LEDs can take
around 300mA so you'd want a medium-power FET. Put perhaps a few
10s of ohms between the PWM output and the gate

eg (although labelled LED this is controlling a motor. ???)

http://www.reuk.co.uk/OtherImages/ne555-pwm-dimmer-circuit.gif

A transistor could be used instead,

http://www.reuk.co.uk/OtherImages/ne555-pwm-led-dimmer-circuit.gif

anything rated at 500mA or better. Select a base resistor for the gain. eg
(roughly) if the transistor has a gain of 300 then 1mA at the base equates 
to
300mA through the transistor. You want the transistor to switch hard so
10mA would be better and is an acceptable drive for the PIC. 470 ohms
to 1k between the PWM pin and the base

You should get some usable results if you Google images for pic pwm motor

> control the contrast that uses negative voltages. Is that really 
> necessary?
> Wouldn't a voltage 0-5V be all that is needed for that?

For a common 16 x 2 yes. The best contrast is often when Vo is just above 0V

wbr 

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