Chill the glass: Place a martini glass in the freezer for a few minutes or fill it with ice water to chill while you prepare the drink.
Combine ingredients: In a mixing glass or cocktail shaker, add the gin (or vodka), dry vermouth, and ice cubes.
Stir or shake: Stir gently for about 30 seconds for a smoother martini, or shake briefly for a slightly cloudier, colder version.
Strain and serve: Discard the ice water from the martini glass (if used), then strain the mixture into the chilled glass.
Garnish: Add two green olives on a cocktail pick or a fresh lemon twist for a touch of brightness.
Enjoy immediately: Serve chilled and sip slowly.