The secret (not really a secret
) is to NOT wash your produce until you are ready to use them. Water is their friend only when they are in the ground. After picking, water just abets their rotting.
I bring home my greens and wrap them loosely in paper towels, then into the crisper. When ready to use, I wash them, and dry them as well as possible, if they're for salad. If I'm sauteing, I just shake them dry.
Depends upon how fresh the veggies are when they go into the crisper, but most of the produce from the Greenmarket will keep up to 2 weeks that way.