Sauteed cabbage works best when your veggie is first sliced, shredded, or chopped. This cooking technique works nicely when you'd like your cabbage to gain a little flavor with the oil or vegetable broth you'll be cooking it in. You can also use wine. Experiment to find the flavors you like best.
Place a frying pan with a lid over medium heat. Add a little extra-virgin olive oil (1-2 teaspoons should do it), or simply use water or veggie broth, or other liquid of choice. When the liquid is hot, add the cabbage. Cook until crisp tender, 5-20 minutes, depending on how you've cut it, and the variety -- green will take less time than red/purple. You can also cook until wilted, depending on your tastes.
Now comes the fun part. Use the Cabbage "Vegan Flavor Matches" to create your very own recipe. Add the foods and flavors you like directly to your pan. Warm. Serve.