The above items are shaken with ice and served up (without ice) in a cocktail glass. The classic garnish is a lime wedge.
Realize, that you can easily find multiple recipes for this very common drink (indeed as Webster said "Common everywhere; widely spread; found in all parts of the world.") - every bar likely has a slightly different recipe. Some of them alter the amounts of the ingredients, others try replacing one of the parts with a similar liquor.
Now, before you go swapping the triple sec for Cointreau or Grand Marnier thinking "this is more expensive than that cheap Triple Sec - it must be better" or trying to decide upon the choice of vodka - normal or a citrus, or the specific brand of vodka you should think about the implications of this and the essence of the cosmo.
The cosmopolitan is a Kool-aid of mixed drinks. It is to be smooth without much of a hint of any alcohol in it beyond the buzz. The flavor should be simple, sweet and very drinkable. Now, Cointreau would be my second choice if you wanted something interesting that diverged from this 'ideal' - the flavor it changes is a much sharper orange than that provided by Triple Sec, though still remaining sweet. On the other hand, Grand Marnier has a spicier and more bitter orange flavor than provided by Triple Sec. It still remains an interesting flavor for someone curious about the possibilities, however it even more significantly differs from the essence of the cosmo.
With respect to the vodka, a citrus flavor does complement the flavor of the drink nicely if it is available. That said, I'd avoid the more 'distinct' vodka flavors such as Absolut, or Skyy (and if it comes in a plastic bottle, just forget about even picking it up off the store shelf). These vodkas have a 'harsh' flavor that once again detracts from the Kool-aid-ness of the cosmo. Instead, I would tend to recommend Stolichnya, Smirnov, or (my preferred) Ketel One.
Other forms of the Cosmopolitan include the Blue Cosmopolitan which uses Blue Curaco (another orange liquor) instead of Triple Sec - furthermore, the cranberry juice is replaced with grapefruit juice (this is to be blue - not purple).