Braised Swiss chard is very similar to sauteed Swiss chard except you're going to brown the chard first, and then add liquid. Cooking it in this liquid will help to break down many of the tough fibers inherent in chard leaves and their stalks.
Personally, I prefer NOT to use this method because I feel a lot of the nutrients are cooked out of the veggie. But you should decide for yourself which technique works best for your needs.
You can use the stalks or not. But if you DO, then you can just leave them attached to the chard.
Place a frying pan with a lid over medium heat. Add a little extra-virgin olive oil (1 teaspoon should do it). When the oil is hot, add the whole chard, or just the leaves if you don't like the stalks. Stir and let cook until mostly browned.
Add water (or veggie broth) until it comes halfway up the side of the chard. Cover and let cook in this liquid until tenderized to your liking. Drain liquid.
Now comes the fun part. Use the Swiss Chard "Vegan Flavor Matches" to create your very own recipe. Add the foods and flavors you like directly to your pan. Warm. Serve.