Cover the entire concrete area to be demolished with a heavy sheet of plastic. This will prevent any pieces from flying up and damaging windows or your home.
Use a sledgehammer to break up the concrete into smaller pieces. Before you can dig up the concrete it will need to be broken down into more manageable pieces. One person should be in charge of using the hammer to break up the concrete and the other person should be in charge of digging up the pieces.
Use a crowbar or shovel to help dig up and pry away the broken pieces of concrete. When the pieces are in manageable sizes, lift them out of the area and deposit them in a waste receptacle.
Work your way from one side of the concrete area to the other, hammering and digging to remove the entire concrete object. It is a good idea to work on small sections at a time to optimize the efforts.