To make watermelon juice, process chunks of fresh watermelon in your blender until liquefied. Pour through fine mesh strainer if there were any seeds or solids.
To make watermelon limeade, combine watermelon juice, lime juice, and simple syrup in a pitcher. Add ice. Serve immediately or allow ice to melt a bit, stir, and then serve.
Notes
If you don't have simple syrup on hand, its easy to make. Just combine equal volumes of water and sugar in a saucepan and heat while swirling just until sugar dissolves. Cool before using and store in air tight container in the refrigerator.