To wilt tender greens, pile them in a skillet (preferably nonstick), turn the heat on, and toss the greens with tongs until they're all collapsed and moistened. If your greens are very dry at the start, you'll need to add a tablespoon or so of water to your pan, but usually the little bit of moisture left clinging to the leaves after washing is enough. Even then, some greens (like spinach) will give off a lot of moisture when wilted, and you'll need to drain them in a colander before proceeding with your recipe so that water doesn't dilute your finished dish. For the simplest dishes (like Wilted Tender Greens with Orange & Ginger), I take the drained, wilted greens and add them back to the skillet, where, in the meantime, I've sauted a few flavorful tidbits in a little oil or butter. Tossed together, the result is delicious. Wilted greens are also a handy base for baked gratins, pasta fillings, or quiches and tarts.
To braise heartier greens, wilt them first in a little fat and finish cooking in liquid. To start the process, sauté aromatics like garlic and ginger or onions and pancetta in a little oil or butter. Add your greens and stir until they're all wilted; then add just enough liquid (like chicken or vegetable stock) to cover the greens. Simmer the greens, covered, until you like the texture. Depending on the age of the greens and your taste, this could be anywhere from 8 minutes to half an hour (or more if you're cooking with tough, older greens). After braising, you can uncover and boil off the remaining liquid if you want to serve the greens alone, as a side dish (see Garlicky Braised Kale). Or you can add cooked pasta, rice, potatoes, beans, or meat to the liquid for a full meal (I add sliced beef to Spicy Mustard Greens with Asian Noodles).