To prep your greens, first strip the leaves from their stalks. (This includes any pre-chopped greens, which are often full of stalks.) Discard or save them for another use; stalks are edible but are not used in this recipe.
Rinse the leaves well in cold water, even if they are bagged and prewashed, discarding any discolored ones. (There is nothing worse than sandy greens, and I have had some in restaurants!) Stack and roll the leaves, then cut them into 1-inch-wide ribbons. Or if you are fond of the tearing method, tear bits of leaves apart instead of cutting.
Heat the oil in a large pot over medium heat. Stir in the onion and garlic. Cook for 6 to 8 minutes, stirring often, until the onion is translucent. Season with the salt.
Add your ribbons (or torn leaves) of greens to the pot a handful at a time. As they wilt down, add just enough of the broth to keep the greens from scorching. Add a little more liquid each time as they cook down (they should not be completely submerged, however). Cook the greens, uncovered, for 5 to 10 minutes, until they are tender but not mushy. Taste and season with more salt if necessary and/or pepper and sugar.
Serve hot, with some of their pot likker.