There are dozens if not hundreds of eggnog recipes. The classic is:
Put cracked ice into a cocktail shaker and add 2 measures rye whiskey (rum or brandy, if you prefer), 4 measures milk, 1 egg and 1 teaspoon caster sugar. Shake vigourously until a mist forms on the outside of the shaker, then strain into a chilled glass. Sprinkle with a little finely grated nutmeg and serve.