Chill the glass. Place a martini glass in the freezer for 5–10 minutes, or fill it with ice water until frosty.
Measure the ingredients. Add the gin or vodka, dry vermouth, and olive brine to a cocktail shaker or mixing glass. The mixture should look mostly clear with a slight cloudy tint.
Add fresh ice. Fill the shaker about three-quarters full with ice so the ingredients are completely surrounded.
Shake or stir. Shake for 15–20 seconds for an extra-cold martini, or stir for about 30 seconds if you prefer a crystal-clear drink. The shaker should become very cold and frosty.
Strain the cocktail. Empty the chilled glass and strain the martini into it. Use a fine mesh strainer if desired for a smoother finish.
Garnish and serve. Add three green olives on a cocktail pick and serve immediately while the drink is ice cold.