Place the mint leaves and 1 tbsp. of the simple syrup (cooled) in the glass, then squish it all around with a spoon (or whatever appropriate utensil you can find) for 20-30 seconds, until you can smell that good minty smell.
Cut the lime in half, getting rid of the seeds as well as you can. Squeeze the juice out from both halves into the glass, then drop one half into the glass.
Pour in the rum and stir.
Add plenty of ice, then top off the mixture with club soda. Garnish with a sprig of mint and enjoy!
Make simple syrup: Heat equal parts sugar and water in a saucepan until just before boiling and stir until the sugar has completely dissolved. Make up a big batch, say a cup of sugar and a cup of water, than toss it in the fridge. It'll easily keep for a couple of weeks, during which time you'll be able to whip up mojitos at a moment's notice, to the delight of your very fortunate friends.