When I taught cooking classes in Indiana, my class on the sauté was probably the most useful, and one of the most popular. The sauté is the restaurant's mainstay. Sautés are almost infinitely adaptable, creating a wide variety of dishes that can be cooked (and served) quickly.
A sauté is a dish in which the ingredients are sautéed. Liquid of some sort may be added, either as a cooking medium, or at the end to deglaze the pan and create a sauce. Almost anything can be used in a sauté, although one would prefer ingredients that will cook quickly, or part of the point would be lost. Chicken, veal, pork, and lamb are frequently used. Beef may also be used, provided that it is a sufficiently tender cut, or has been tenderized.
Sautés are so adaptable that they are the ultimate "create a dish" opportunity. Consider a chicken sauté. You can add white wine and herbs. You can add cream. You can brown the chicken, then add the liquid and let the chicken poach in it, or you can cook the chicken entirely in the butter, remove it, and use the liquid and herbs to deglaze the pan. You can add mushrooms, artichokes, asparagus. You can add almost anything you want.
There are a few things you need to know. First, if you want that beautiful golden color, the only thing that will get it for you is butter. Butter as you buy it, however, will burn. See my article on how to clarify butter, and use clarified butter. Second, whether you're using liquid as a cooking agent or to deglaze the pan at the end, you don't need much. You'll use more if it's a cooking agent, since part of it will evaporate, but no more than a half cup at most. If you're deglazing the pan, you'll need no more than a few tablespoons.
If you deglaze with cream, know that not all "heavy creams" are equal. It's nearly impossible these days to find real heavy cream, which should be yellowish and thick right out of the carton, but use the richest cream you can find, since you want it to thicken and carmelize. If you can get it, double devon, imported from Britain, and as thick as butter, is excellent for deglazing a sauté. You only need a couple of spoonsful. It melts as soon as it hits the hot pan, then almost immediately begins to turn golden and thicken.
Always turn the heat as high as possible to deglaze. You want to both allow the liquid to pick up all the flavor and flavorful bits from the pan and reduce.
If you have a sauce, you can "finish" it with butter, which will add a gloss and thicken it a bit. Add a tablespoon or so of butter, but do not stir. Rather, swirl the pan as the butter melts, and let it mix itself into the sauce. There is no point in finishing a cream sauce.
A basic chicken sauté would be to brown chicken on all sides in butter over high heat. Turn the heat down to low, cover, and cook the chicken, turning from time to time, until done. Remove the chicken, then turn the heat high and deglaze the pan with a bit of cream, stirring constantly to get all the goodness from the pan into the cream, until it turns golden and thickens. Pour over the chicken pieces and serve.