Place the martini glass in the freezer for at least 10 minutes or fill it with ice and water while you prepare the cocktail. This will help keep the drink cold.
In a mixing glass or cocktail shaker, combine the gin and dry vermouth. Add a generous amount of ice cubes to the glass, ensuring they cover the liquid. Stir the mixture for about 30 seconds to properly chill and dilute the drink. Stirring instead of shaking will keep the martini clearer and less frothy.
Remove the ice from the chilled martini glass. Place a strainer over the mixing glass or cocktail shaker and pour the martini mixture into the glass. This will prevent any ice or residue from entering the glass.
If you prefer a lemon twist, take a strip of lemon peel and twist it over the glass, allowing the oils to release into the drink. Rub the rim of the glass with the twist and drop it into the martini. Alternatively, you can garnish the martini with a green olive on a toothpick.