There are a lot of times that the term sauté is used to mean cooking anything in a skillet but the term is actually very specific. The term originates with the French verb sauter which means "to jump."
This is because very high heat is used and the food should be in frequent motion (or jumping).
Because most foods contain a great deal of water, if a the pan is too crowded the foods will actually steam (see Sweating). To sauté properly, choose a pan large enough that there is at least 1/3 of the surface area of the pan exposed when the vegetables are added.
Most recipes call for lots of fat when sautéing vegetables or the like. This is not necessary if a large non-stick skillet is used. Preheat the pan and add the oil. The vegetables should be added just before the oils smokes and then the heat reduced slightly. The key is to keep the food moving, tossing it frequently to use the oil and pan to full advantage.
This is very easy for something like onions but mushrooms do pose a more specific problem in that they are like little sponges and will absorb any liquid.