Secure the best-looking pallets you can find and if possible get pallets that are uniform in size and configuration.  If the pallet has been handled badly the damage might make the pallet unfit for your project.

Place the 12" 1 x ? piece as far under the pallet as it will reach with at least 6 inches protruding from the front of the pallet.

Place the 4 x 4 on the 1 x ? board within an inch of the first pallet board.  Wedge the pry bar between the 4 x 4 and the pallet board. 

Strike the end of the 4 x 4 with your hammer, and the pallet board will begin to lift from the runner.  The pry bar will finish lifting the board if the board doesn’t pop from the runner. 

Move to the next runner and repeat the process until the top boards have all been removed. Turn the pallet over and start on the bottom boards.

The 4 x 4 will not be useful for removing the bottom boards, so use just the pry bar and hammer to remove the bottom boards.   These boards are usually the most abused and dirty boards harvested from a pallet.

Remove the nails and wash the boards with a 5 to 1 Bleach to water solution to disinfect.