Simple syrup is easy to make. Just put some water in a pan and boil it, throw in sugar. 1:1 water/sugar ratio for thick syrup 2:1 for medium 3:1 for thin. For this recipe you would want the thinner stuff.
I had my first mojito a little over a week back at a restaurant called Mojito's in Louisville, Kentucky. Man, it was DELICIOUS! I was the only one at our table to get one, and I got it based on the recommendations of you fine brothers. After everyone tasted mine, we ended up with a couple pitchers full of 'em!
I watched them closely at azucar last time I went. They put cut up limes and the mint into the glass, then poured plain ol sugar on top. Then you take a wooden muddler and do that downwards twisting motion till its all nice and mashed. Then the bartender added the ice, poured in plenty of rum and topped it with the club soda.
I think there is a little stirring after the rum is added, but everything is made right in the glass, no shakers.