The quickest way to unwrinkle clothes is to use a handheld clothes steamer to loosen the wrinkles in a garment just before you are about to wear it. Heat the steamer up according to the instructions on your device as you get the rest of your outfit ready or do your hair and steam the garment, hanging up on the back of a closet door, for instance, to help the wrinkles drop out directly before wearing it.
Never steam a garment you are already wearing, however, as this could lead to serious burns and skin damage.