Chard is in the same family as spinach and beet greens, and cooks the same way. Use the ribs as well as the greens! The ribs make great quick pickles.
Store chard in the fridge for several days, if not longer. Unwashed greens last longer, so only wash right before you plan to cook. If you want to store greens in the fridge for longer, wrap them in a damp paper towel. Greens also freeze well. Blanch in salted boiling water for 3 minutes, drain and plunge into ice water. Chill for two minutes; drain. Pack in freezer containers or bags.
Cook chard much like you would spinach. Pull the leaves from the stems and chop the stems into small pieces. Put them in the pan several minutes ahead of the leaves to allow them to cook longer. Cook stem until tender but still with a touch of crunch and cook leaves until tender and buttery. Top pizzas with sliced, raw chard leaves and add cooked chard to frittatas, tarts, galettes, or rice casseroles. Or eat fresh as a wrap for your burger or breakfast skillet.