Both should be harvested before frost. Remove the fruit from the vine with a portion of the stem attached. Store on shelves in a single layer so air can circulate around them. Silks will be dry and kernels filled. If milky juices exudes, it is ready for harvest.
Sweet corn has a very short storage life.
Harvest at peak quality, husk to conserve space, and store in plastic bags for no more than 2 days in the refrigerator. Ideal storage is 32 to 40 degrees F and 90 to 95 percent humidity. Merely break off the outer leaves. Swiss chard is a beet developed for its top. A spring planting will provide greens from early summer to the first moderate freeze.