It's amazingly easy and you can use the pure for loads of yummy stuff.
So essentially what you need to do is this:
1) Cut that watermelon off of rind and into small cubes
2) Stick in a food processor and pure (don't worry about the seeds)
3) Pour liquid through a strainer (this is a good time to allow your kids to help!)
4) Put the strained liquid in a container to drink later. You can also pour it into an ice cube tray and freeze or a larger container to freeze and eat later.
5) To make the Aqua de Sandia pour some of the pure into a cup and add water. I liked a ratio of half to half but you can add more or less water to taste. Lime is a nice addition as well. I like using sparkling water. A friend came to dinner recently and we tried it with Absolute Citron for an adult drink that is crisp and fresh tasting.