To saute onions, begin by melting butter or using cooking oil, about 1 ounce of fat per onion, in a pan that is on medium-high heat. After the pan gets hot, add the onions, and cook for five to seven minutes, stirring with a wooden spoon or heatproof spatula. Remove from heat once the edges start to brown.
Another form of sauteing onions, known as caramelizing, takes longer because it uses lower heat. This process makes the onions extra sweet because it breaks down the natural sugars. To caramelize the onions, melt butter in a pan over medium-low heat, and add thinly sliced onions to it. Cook the onions with a cover for about 13 to 15 minutes until they are tender. When they are tender, remove the lid, and stir them on medium-high heat for another three to five minutes.
Before cooking the onion, it is important to cut it in a way suited best for the cooking style. Begin by washing the onion under cold water, and then chopping off the ends, removing the outer skins, and chopping it in half. For chopped onions, place each half face down, cut one way without going completely through the onion, and finish by cutting the opposite way. To slice an onion, place it on its side, and cut it crosswise.