With the various so called Perfect versions of this classic of classics why not weigh in.
First things first, a martini is gin. Not vodka. I like Michael Ruhlman's suggestion that a vodka martini should be called a "vodkatini."
As for the specifics of this recipe, I recommend for full effect, that you have your first one of these at about 5pm just as the sun begins to peak through the cocktail glass. Add some Charlie Christian and you will be just fine. I won't get picky about what type of gin you use but I like a nice simple London dry.
2 1/2 oz. London dry - I like Beefeaters
1/2 oz. Dolin dry vermouth
2 dashes orange bitters
1 large lemon peel
Combine the gin and the vermouth -make sure your vermouth is fresh and cold- right out of the fridge. Yes make sure to refrigerate your vermouth. So toss out that 5 year old stuff hiding in the back of your liquor cabinet.
Add 2 dashes of orange bitters. If the bottle of bitters is brand new maybe a few more. Add as much ice as will fit in your mixing glass. All the way to the top... a llittle more...there you go.
With a nicely weighted stirrer stir the drink for about 20 seconds as quickly and smoothly as you can. Strain into a chilled coupe, fresh from the freezer.
Take a nice, big piece of lemon peel and fold it in half peel side out, length wise, directly over the drink. You should hear and feel a little crack as the oils sprays over the top of your drink. That's the good stuff. Run the outer edge of the peel around the rim of glass. Drop it in the drink. Serve.