Leaves and stalks are often treated as two different vegetables.
Stems are typically braised, leaves are used as you would spinach--in soups, as braised greens, with eggs, rice, lentils and in savory tarts.
Related to spinach, beets and quinoa.
Store chard, like all greens, in a plastic bag in the refrigerator.
RECIPES
Braised Chard with Cilantro:
1 big bunch of chard, leaves sliced into 1 inch wide ribbons
1 1/2 cups of chard stems, diced
1 onion diced
1/2 cup chopped cilantro
1/3 cup olive oil
1 teaspoon paprika
1 garlic clove pounded with 1 teaspoon salt
salt and pepper to taste
Place all the ingredients in a wide, heavy pot with a few pinches of salt. Add 1/4 cup water, cover tightly and cook over low heat for 45 minutes. Check once or twice to make sure there is enough moisture. If anything is sticking, add a few tablespoons of water. When done, taste for salt and pepper. (Vegetarian Cooking for Everyone by Deborah Madison)
Other recipe links:
Trouchia (Chard and Onion omelet)