How to connect PWM output from a dsPIC MCU to 12V LEDs?
The easiest solution is to use N-channel MOSFETs.  I assume that your controller is running at 3.3 Vdc - that means that you need MSFETs with low turn-on voltage.

You can't use a chip like a 2803 because of the load current you want to use.  The 2803 is rated at 500 mA absolute maximum but you would never want to run it that high - the saturated voltage on that chip is really high and any significant amount of current leads to large amounts of heat that the package can't dissipate.

My favourite type of NOSFET for your application is a class called "Trench FET".  Several manufacturers make these - the names they call them are all different but they all have the word "Trench" as part of the name.  Your favourite supplier should be able to sell them to you.

The reason this class of MOSFET is ideally suited for your application is that they have very low Rds-on values and very low Gate turn-on voltage.  The Gate can be driven directly by your microcontroller at low-frequency PWM speeds.  

Their main limitation is that they can't handle high voltages on the Drain but your supply voltage is well within their operating range.