You have to have the colors blend together, Black goes with everything but with turquoise, i think the best bet is a dark brown. If you could find a blouse that is the same color of the shoes and then some dark brown slacks i bet it would look totally awesome!!
Dress up your shoes with an outfit that is more neutral in colors. A nice pair of blue jeans, dark or light wash, paired with a black, white, cream, or other neutral color would bring a fantastic pop to the shoes.
Any outfit with really basic colours will work. For instance if you wore black pants with a purple shirt that would go really well with turquoise. You could also wear jeans with a blue shirt and so on.
A gauzy yellow print two piece outfit with some turquoise in it is good. Black pants or skirt with a blouse with turquoise in it is nice. A turquoise print bag with a solid color outfit is a good choice. Even a kelley green skirt with a kelley green and turquoise print top is an option.