This is how I cut up a watermelon, although if it's larger, I'll cut it in half to have a stable surface while cutting off the rind. The post from Fifteen Spatulas also has a delicious recipe for watermelon-lime slushies.
This tip is especially useful for those of you that don’t have any nails to dig into the tough skin of an orange. With a few clever cuts of a knife, you can peel an orange and eat it without juice dripping all over your hands. But best of all, it’s FUN! (http://www.listotic.com/36-genius-kitchen-tips-and-tricks/6/)