Muddle limes and sugar in a cocktail glass, using a muddler or wooden spoon.
Add cachaça and ice. Stir well.
Notes
If you don't like your cocktails very strong you can reduce the amount of cachaça. Increasing the amount of sugar will help sweeten the drink as well. For strawberry caipirinha, substitute strawberries, sliced and quartered, in place of lime. You can keep some lime, if desired, for flavor.