Although the "proper" way to make a Caipiroska is a matter of quite varied opinion, this is the basic recipe:

Use an old fashioned or highball glass.

Squeeze juice from lime wedges into the glass. Place one of the lime wedges into the glass and add sugars. Muddle sugar with lime wedge. Be careful not to overdo the muddling of the lime rind as it may introduce too much of the essential oils from the lime and make the drink too bitter. Pour in vodka and stir well until the sugar is dissolved. Add crushed ice and stir to melt some of the ice. Garnish with lime slice or wedge and serve. Some mixologists advocate placing all of the lime wedges into the glass without squeezing them, adding the sugar and muddling the lime wedges and sugar together well to release the juice and essential oils from the limes. Another variation is to use either all white sugar, or all raw or turbinado sugar. Using all white sugar will result in a clearer drink, while using raw or turbinado sugar will result in a more or less tan-color drink. As with any cocktail, the proportion of ingredients and subtleties of technique will result in differing nuances of flavor.