With a chef's knife or your hands, separate leaves from stems. Cut stems crosswise into 1/2-inch pieces; set aside. Stack leaves, roll them, and cut crosswise into 1/2-inch ribbons. Set aside, keeping separate from stems.
In a large heavy pot or Dutch oven, heat oil over medium heat. Add garlic and cook until golden, about 1 minute. Stir in chard stems; reduce heat to medium-low, cover, and cook, stirring occasionally until stems have softened, 3 to 5 minutes. Add damp chard leaves and 1/2 cup of water. Cover and cook, stirring occasionally, until the greens are completely wilted and tender, 3 to 6 minutes. Season with salt and pepper. Serve immediately on a platter or in a bowl, with lemon wedges on the side.