Vodka Martinis have started being in existence long after the gin-based drink was already very popular, and have been created as a variation of the latter. Regardless, the Vodka Martini has gained more and more ground, especially in recent years, resulting in more and more people believing the martini to be first and foremost a Vodka based cocktail, and expecting to receive this kind of drink when ordering in a bar or restaurant.
Perhaps the most famous Vodka Martini drinker is James Bond, who has made the expression "shaken, not stirred"(as referring to how he prefers his martini) known throughout the world. What not many know is that the expression can be considered blasphemous by Martini purists, who claim that a well made martini should be stirred, and by no means shaken.
The Vodka Martini is made by replacing the Gin in the original recipe with Vodka. You take four parts of Vodka, for instance, 2 ounces, and one part of Vermouth, that is 1/2 of an ounce(either red or white, depending on whether you want your martini to be regular or drier, as the white vermouth is far drier than the red one) and stir it with some ice cubes or crushed ice. Then, you strain the mix and pour it into a cocktail glass, very careful about not getting any of the ice in there. You can then add an olive (rinse the olive before putting it into the glass, so that there are no leftover traces of vinegar on it), or a piece of lemon peel (for a softer taste). The quantities of Vodka and Vermouth in your martini can vary, and you can change reports, for instance to an ounce and a half of Vodka and three quarters of an ounce of Vermouth, depending on your preference. You can also decrease the amount of vermouth in your Martini to a point where only a slight hint of it exists, for flavoring purposes, making your Martini extra dry.