1/2 oz. lime juice
2 oz. vodka
6 oz. ginger beer
3 mint leafs
1. Squeeze lime juice into a Collins glass (or Moscow Mule mug) and drop in the spent shell.
2. Add 2 or 3 ice cubes, then pour in the vodka and fill with cold ginger beer (not ginger ale, although what the hell).
3. Serve with a stirring rod.
George Sinclair's 2007 article on the origin of the drink quotes the New York Herald Tribune from 1948:
The mule was born in Manhattan but "stalled" on the West Coast for the duration. The birthplace of "Little Moscow" was in New York's Chatham Hotel. That was back in 1941 when the first carload of Jack Morgan's Cock 'n' Bull ginger beer was railing over the plains to give New Yorkers a happy surprise… The Violette Family helped. Three friends were in the Chatham bar, one John A. Morgan, known as Jack, president of Cock 'n' Bull Products and owner of the Hollywood Cock 'n' Bull Restaurant; one was John G. Martin, president of G.F. Heublein Brothers Inc. of Hartford, Conn., and the third was Rudolph Kunett, president of the Pierre Smirnoff, Heublein's vodka division. As Jack Morgan tells it, "We three were quaffing a slug, nibbling an hors d'oeuvre and shoving toward inventive genius". Martin and Kunett had their minds on their vodka and wondered what would happen if a two-ounce shot joined with Morgan's ginger beer and the squeeze of a lemon. Ice was ordered, lemons procured, mugs ushered in and the concoction put together. Cups were raised, the men counted five and down went the first taste. It was good. It lifted the spirit to adventure. Four or five days later the mixture was christened the Moscow mule...
The Moscow mule is almost always served in a copper mug. The popularity of this drinking vessel is attributable to Martin, who went around the country to sell Smirnoff vodka and popularize the Moscow mule. Martin asked bartenders to pose with a specialty copper mug and a bottle of Smirnoff vodka, and photographed a Polaroid picture of them. He took two photos, leaving one with the bartender for display. The other photo would be put into a collection and used as proof to the next bar Martin visited of the popularity of the Moscow mule. The copper mug remains, to this day, a popular serving vessel for the Moscow mule.
According to a 1942 Insider Hollywood article, the Moscow mule was most popular in Los Angeles, where it originated. The Nevada State Journal (12 October 1943) reinforced the mule's popularity in reporting: "Already the mule is climbing up into the exclusive handful of most-popular mixed drinks". It became known as a favorite drink of Reno casino owner William F. Harrah. In his book Beat the Dealer (1964), Edward O. Thorp did not name the Tahoe casino where he thought he had been poorly treated as a card counter. Instead, he wrote, "Immediately I had a Moscow mule", subtly hinting that the location was Harrah's Lake Tahoe, due to Harrah's then well-known proclivity for the drink. - Wikipedia