It may seem labor intensive and time consuming but making these really isn't that hard and doesn't take too long once you get the hang of it. You could even carve deeper into the apple when you remove squares so that the colored squares stand higher for a more dramatic look.
-small bowl of water with a few drops of lemon juice mixed in to stop the apple from browning
-a succulent and/or luscious apple
I like the way red apples look with the checkerboard pattern but you could use green as well. When choosing an apple be sure that there will be nice contrast between the skin and the flesh so that the pattern shows up well (those weird yellowish apples are not recommended).
Of course you could try using a half of an apple instead of a quarter slice but I like to work in quarters so if I mess up I only mess up a quarter wedge.
After all the lines are scored into the apple, give another dunk in the lemon-water.