Combine sugar and water in a small pan over medium heat; cook until sugar dissolves. Remove from heat and toss in mint sprigs. Allow to steep for about an hour, then chill syrup.
In shaker or tall glass, add 8-10 mint leaves, 2 lime wedges, and a dash of simple syrup. Then muddle until well smashed.
Fill shaker with ice, then add Rum and shake.
Pour into tall glass and top with 1-2 oz. club soda.
If I'm making Strawberry Mojitos, I slice strawberries then sprinkle them generously with sugar and a splash of juice (any kind); cover them and refrigerate for an hour or two....voila strawberry simple syrup.