Begin by chilling the martini glass. You can either place it in the freezer for at least 10 minutes or fill it with ice and water while you prepare the cocktail. This step ensures a cold martini.
In a mixing glass or cocktail shaker, combine the gin and dry vermouth. Add a generous amount of ice cubes to the glass, making sure they cover the liquid. Stir the mixture for about 30 seconds to properly chill and dilute the drink.
Strain the martini mixture into the chilled glass. To do this, use a strainer placed over the mixing glass or cocktail shaker while pouring.
Complete your martini by garnishing it. If you prefer a lemon twist, take a strip of lemon peel, twist it over the glass to release the oils, rub the rim of the glass with the twist, and drop it into the martini. Alternatively, you can garnish with a green olive on a toothpick.