First cut off the ends of the limes and then cut them into eighths. Put the limes with the sugar in a suitable glass and pestle. Top up with crushed ice and add the cachaca. Put in 2 straws and serve.
Tip for crushed ice: Either you put ice cubes in a bag (or kitchen towel) and crush it with a hammer or you use a commercially available ice crusher.
There is one made of plastic for about 10 € (but they are no good). Others are made of metal and cost around € 20. Then there are also the electric powered crushers for around 40 €, which I would recommend.