Stir with ice. Strain into a cocktail glass.
You can use bourbon whiskey instead of rye.
One of the things that fascinates me most about the Manhattan, is that it is one of the few pre-prohibition cocktails which survives to this day with its recipe, for the most part intact. As would any drink of that day called a cocktail, it still includes bitters, an aspect that its younger sibling, the Martini, can no longer say. Also unlike the Martini, the ratio of spirit to vermouth is usually fairly similar to what would have originally been used. I would even hazard to say that a modern day Manhattan would be completely recognizable to a bartender from the 1880’s.