Cut the watermelon in half
Cut the halves in half, in the other direction (ending up with quarters)
Cut the quarters into half-moon slices
Cut the flesh up into chunks and fill the blender with them
Smash the chunks in the blender with the muddler (or whatever) until they're all smashed up
Run the blender on a "liquify" setting, or something equivalent, until it's a liquid
Through the normal strainer, pour the watermelon liquid into the 2-quart pitcher -- or the smaller pitcher if you want less pulp
Use the muddler (or whatever) to get more juice out of the pulp remaining in the strainer
If you're going for less pulp, pour the juice from the smaller pitcher into the 2-quart pitcher, through the double strainer
Repeat the relevant steps above until you feel you're done