To sauté an ingredient means to fry it quickly in a little bit of hot fat. This technique works best in a pan with a heavy bottom.. Heat conductivity varies among metals, but cast iron, stainless steel and copper pans all conduct heat well and evenly. 

Sautéing begins with a hot pan and hot fat.  Before you add anything else to the pan, heat it up with the fat being careful not to get either so hot that they start to smoke. When choosing a fat for sautéing, keep in mind that animal fats such as butter, chicken fat, duck fat and pork fat have lower smoke points then plant-based fats. Animal fats begin to break down and smoke between 300 and 350 degrees F. Olive oil breaks down and smokes early too, but some can reach 400 degrees F before doing so. Peanut oil smokes at a higher temperature (up to 440 degrees F) and if you want to get your oil to 450 degrees F and above, soybean and rice bran oil are good choices. I recommend stocking soybean, coconut, grapeseed or rice bran oil in your kitchen pantry, exclusively for cooking at high heat; I like grapeseed. When health is a consideration, I recommend a plant-based oils for high temperature cooking.  

One of the most important aspects of mastering this technique begins with the knife.  In order for the ingredients in the pan to cook in the same amount of time, they must be cut in uniformly small--or large--pieces. When you are sautéing more than one vegetable, it may be necessary to blanch one or more of the ingredients ahead, to cut down on the amount of time it takes to cook the ingredients through and to ensure that they will be finished at the same time. 

After heating the fat in the pan to a high temperature (just below smoke point), add the seasoned ingredients and begin to cook. Move the ingredients around in the pan to ensure that they don't stick and relying on a sensory approach to the process, watching (and smelling) as the ingredients transform from raw to evenly browned without overcooking.