There are many different ways to take apart pallets in order to use the wood for something else. I have found that prying them apart causes a lot of damage to the wood and is a lot more work then is necessary. So, my preferred method is to cut the pieces apart using a sawzall.
All you have to do is cut through the nails that are holding it together and you are good to go (with minimal damage to the wood). If you want you can pop the remaining parts of the nails out of the wood.
Just take the sawzall and cut right between the piece you would like to save (the top piece) and the thick frame. Try to cut just the nails and not too much of the wood. Once you get the hang of it it will go really fast.