Here is the recipe I use:
2 tablespoons (1 ounce) fresh lime juice
2 heaping teaspoons superfine sugar
1 cup crushed ice
12 fresh mint leaves, plus 5 small sprigs for garnish
1/4 cup (2 ounces) white rum
2 tablespoons (1 ounce) club soda
In a glass, stir together lime juice and sugar until sugar dissolves. Add mint leaves and muddle until the leaves are broken up and the oils mix in with the sugar. Add 1/4 cup crushed ice. Gently stir for 15 seconds, then add rum, remaining crushed ice, and club soda. Gently stir for 5 seconds, then tuck mint sprigs into top of glass and insert tall straw.
And a picture:
If you want to make a raspberry mojito, all you need to do is buy the raspberry flavored rum and sub it for the white rum. Cruzan makes it, and probably bacardi does too. You could also crush some raspberries with the mint leaves and add some fresh raspberries to the finished drink as a garnish to fancy it up.