I don’t have a Martini now, but if I did, this is how I would have made it:
In a chilled martini glass, pour half a nip of vermouth over two ice cubes. Swirl gently, letting the vermouth coat the glass; ditch everything but the glass into the sink. Add three frozen nips of Tanqueray, three drops of bitters, and a twist of lemon.
If you haven’t had the foresight to keep your gin in the freezer, you may use a seperate mixing glass. Fill the mixing glass with ice, add the half nip of vermouth, coat the ice cubes, discard the vermouth. Add the gin, bitters, stir very gently, and strain immediately into your chilled glass.
Some people like vodka martinis. I prefer my vodka neat, straight from the freezer, in a shot glass. In the former East Germany, I learned to drink vodka like this, with a cola chaser. That was an interesting evening.