A Caipirinha (kai-pur-een-ya) features cachaça, the Brazilian liquor made from sugar cane. I suppose the most obvious comparison is to rum, although I think cachaça often has a more complex and appealing flavor. This drink certainly won't be the same if you substitute rum.

Traditionally for a caipirinha, one muddles limes, adds simple syrup (or sugar) and cachaça, shakes and pours the whole deal into a rocks glass filled with ice. That works fine, of course, but for a similar flavor and smoother texture, I recommend you first juice the lime, strain out the pulp, and go from there. Whether you stir it or shake it depends mostly on your barware inventory; stir if you're using a martini glass, but shake if you're going with a rocks glass.

The line-up:
1 shot cachaça (white; unaged)
juice of half a lime, strained (about a half shot)
dab of simple syrup or agave nectar

Stirred:
Drop a thimbleful of simple syrup or agave nectar in the bottom of a frozen martini glass. Add the cachaça and lime juice. Stir until the syrup/agave incorporates into the liquids. Garnish with a lime twist and ice cube. For a lighter, more voluminous and effervescent drink, add club soda.

Shaken:
To prepare for a rocks glass instead of martini glass, add the liquids and syrup/agave to a shaker along with three ice cubes, shake and pour into a rocks glass filled with ice. Do not shake with club soda; add the soda after you pour out the drink (if at all).