A classic gin martini is made with gin, dry vermouth and lemon. A classic vodka martini is made with chilled vodka and dry vermouth and is garnished with olives or a lemon twist.
To make a classic gin martini, crack a large cube of ice into pieces using the back of a stirring spoon. Repeat this process until you have a mixing glass filled with ice. Then, add 4 ounces of gin and 3/4 ounce of dry vermouth to the mixing glass. Stir rapidly in a circular motion about 50 times, until the outside of the shaker becomes cloudy. Then, strain the mixture through a strainer into a chilled glass. Remove a small amount of peel from a lemon, wipe it over the rim of the glass, and then float it in the martini.
To make a vodka martini, swirl a little dry vermouth around in the inside of a chilled martini glass. Dispose of the vermouth, and set the glass aside. Next, fill a cocktail shaker with ice, and add 2 ounces of chilled vodka. Swirl or stir the vodka around, and then strain the drink into the martini glass. Garnish with olives, a lemon twist or a few pieces of ice if desired.