Ah, the Martini. The quintessential "cool" cocktail, staple lunch item of businessmen throughout America, and icon of the heroes of the Jet Age.
The Martini's history is somewhat murky. Some attribute it as a streamlining of the more complex "Martinez", first made in Martinez, California in the late 19th century. The New York Times claims that the Martini originated in 1912, in the Big Apple's Knickerbocker Hotel. Personally, I think New York's getting greedy.
The Martini really began to clinch it's mystique when it became know as the drink of choice of such personalities as Ernest Hemingway, Dean Martin, FDR, Dr. Robert Oppenheimer, F. Scott Fitzgerald, Truman Capote, Winston Churchill, and of course, Ian Flemming's James Bond.
There are two primary types of martini, the Gin Martini and the Vodka Martini. Both can be used in the same ratios, but the preparation differs slightly between the two. The ratios vary wildly depending on whom you ask, but I'm more a classic martini drinker.
To make the Martini you'll need 3 parts either gin or vodka, and 1 part dry vermouth.
If you're making a gin martini, pour the two ingredients into a shaker with ice and stir. Strain it into a cocktail glass and garnish. You'll want to have both ingredients chilled before hand. If you shake the drink, you'll kill the vermouth, and bring the gin too far to the front.
If you're making a vodka martini, place the two ingredients into a shaker filled with ice, shake vigorously, then strain into a cocktail glass and garnish. Keep the vodka cool, but not chill, so that the temperature differential will lower the bite of the alcohol. The key is to shake it hard to maximize the chilling at that point. If the vodka's too cold at first, then it'll overpower the vermouth, but if the drink doesn't get cold enough by the time it's drunk, it'll taste a little too thick.
The garnish is traditionally a martini olive on a toothpick. Some prefer a lemon twist, some a Marciano cherry. Myself, I go for three olives. Go with your gut, but don't be afraid to try new things. Once you've finished garnishing, take a sip, and imagine yourself in a tuxedo.
The amount of each ingredient used will vary. The modern martini is 5:1 gin to vermouth. The european martini is 6:1. The Old Martini is 2:1. Some recommend coating the ice cubes with vermouth to impart flavor, without actually adding vermouth to the drink. Some of the extra dry martinis might go as high as 10:1 or 15:1. Winston Churchill's martini was famed for being made from 3 parts gin, and a glance at a bottle of vermouth from across the room.
There are a ton of variations on the martini. I'll cover just the bare bones here. A perfect martini uses 1/2 part dry vermouth and 1/2 part sweet vermouth. A dirty martini adds some olive juice to mask the alcohol. A naked martini is made with no ice, but the ingredients and glass chilled.