Muddling. Technically, it's combining ingredients in the bottom of a mixing glass (typically with an instrument made for this purpose, called a....wait for it....muddler) before the rest of the liquid ingredients are added to make a cocktail. Following shaking and stirring, it is probably the most typical action needed to create cocktails. And it's one which I think is done incorrectly more often than not.
Like any action related to bartending, it can be argued there is no right or wrong way to do anything. Slow shake, hard shake, Japanese shake, lazy shake - which way a bartender performs any action is dependent upon their experiences and preferences, and of course those vary widely. So I am not saying that there is a "wrong" way to muddle ingredients for a drink. However, the basic goal of muddling is to extract desirable flavors from the ingredients being muddled. And it therefore makes sense that different ways of performing this action accomplish this goal better than others.
Of what I have read and seen, a deliberate, GENTLE muddling fits the bill just fine. You're trying to coax the essential oils, juices, and flavors from the ingredients, not beat the living crap out of them (I saw one obviously 'roided-up bartender muddle limes and mint for a mojito like he was driving a steel pole into the ground - he was SWEATING afterwards). And ingredients like mint, which tend to bruise and discolor if too harshly treated, hold up better when not abused like the Washington Redskins on Sunday afternoon.
Which leads us to the Caipirinha (kai-pee-reen-ya), a drink so simple it's almost criminal how good it is. I think the only reason this isn't much more popular than the mojito is that almost no one is confident they know how to pronounce it (or its main ingredient, cachaca (ka-sha-suh)). The muddled lime stays in the glass, there is no shaking required, no bar instruments other than something to perform the muddling with need be brought out - cut lime, add sugar, muddle, add ice and cachaca, quick stir, done. And it's gorgeous to look at - perfect for those warm spring cocktail parties or hanging out on newly opened bar patios.
.5oz simple syrup (or barspoon of sugar)
one lime, quartered
Muddle the lime and sugar in the bottom of an old fashioned glass. Add cracked ice to fill the glass. then add cachaca. Stir well.