I have various Martini cocktail recipes but none called 'dirty'; I found the following at cocktails.about.com ... the 2nd one sounds deadly, never mind dirty!
1 1/2 oz. Gin or Vodka
Splash of Olive juice
Dry Vermouth (if desired)
Directions:
Stir over ice.
Strain into a chilled cocktail glass.
Garnish with olives.
OR ...
2 oz Gin
1/2 oz Dry Vermouth
1/8 tsp Absinthe
Stir well with ice. Strain into a prechilled cocktail glass.
Some bartenders pour a soucon of Absinthe into the glass, swirl it around and then add the martini.