Soak a washcloth in water and apply dish/hand soap to it liberally, and then scrub the affected areas of the mattress down thoroughly. If the mattress has been sitting unused for a while, it is a good idea to scrub the whole surface down to sanitize it completely.
Spray the mattress with a citrus cleaner or soak a washcloth in a detergent/water mix (1/8 cup detergent per gallon of water) or vinegar/water mix (8 cups vinegar per gallon of water). Dab at the affected areas of the mattress, and then scrub it down thoroughly.
When you are done scrubbing the mattress, open a window or set it outside for several hours to allow it to dry.
Give the odorous areas of the mattress a thorough dusting in baking soda and allow it to sit, undisturbed, for approximately 8 to 10 hours, then take the mattress outside and shake it off completely to remove the baking soda.
Move the mattress to a sunny area and leave it there for several days (a sun porch with large windows is perfect). After it has had at least a day of total sun exposure (24 hours), vacuum the entire surface thoroughly. This will remove the now dried out mold/mildew spores as well as any dust mites. Follow steps 1 and 3 or 2 and 3 to finish sanitizing your mattress.