Of course, you can ignore this fact and simply cook the stalks and leaves together (as you would with turnip greens). However, I prefer to toss the cut stems in a light coating of salt and olive oil, and roast them in a 425 degree oven for 15 minutes.
The leaves are lovely, heavy and substantial. Today I prepared them (one bunch of chard) in a saute pan with a 1/2 cup of chicken broth and two finely sliced cloves of garlic. After bringing the stock to a boil, I lowered the heat and allowed the greens to simmer, covered, for about ten minutes. After simmering, I raised the heat briefly and added a tablespoon of white wine vinegar before serving.
The taste was powerful, just the transport to summertime that I have been needing. I served the chard for lunch alongside a fluffy couscous and cubed chicken, but the marriage possibilities for this vegetable are truly endless (although I would recommend not overshadowing the chard with the main course).