First, fill your glasses with ice and split the club soda into the two.
Next, in your shaker, add the mint leaves, sugar, and blueberries*. Use a muddler (or the end of a wooden spoon) to muddle well. Add the lime juice and rum; shake vigorously.
Now, pour the drink from the shaker into the glasses, give it a gentle stir. Add more mint leaves, a lime wedge, more blueberries, or whatever you desire to garnish the glass.
*This is the way I made these and they were perfect. If you are worried about the consistency, place the blueberries in a blender or food processor, then add them to the shaker with the lime juice and rum.