This is up to you. The most recognizable outfit for a Marilyn costume is the white dress that is prone to blowing around. Wear a pair of long gloves and heels. Douse yourself in jewelry, namely fake diamonds or pearls.
The short blonde bob is a must, even if Marilyn was a natural redhead. You can't avoid buying a wig for this one if you don't have the hair for it. A tip is to look for cheap wigs that are sold for teen costumes. They will fit adult-sized heads and cost a little less.
Bright red or pink lipstick. Over-do the mascara on the eyes, but not too much color on the lids. Use an eye pencil or liquid mascara to add a beauty mark just at the upper corner of your lip.
Bonus Costume Tip:
This costume doubles as Ginger from Gilligan's Island. all you have to do is change the hair color and wear a Hawaiian lei and a flower in your hair.