I learned this from a chef at a Fuhrman immersion last fall.
Heat a pan up. I use a stainless steel pan, no need for non-stick coating. I put the dial to medium, number 5, on the electric stove. Chop up your onion. Throw it in the pan. It should sizzle and start browning. Add the lid right away. This will trap the moisture that's released and keep it from browning too quickly. Stir a lot. Then when it browns some but isn't burned yet, you can add some water and/or other veggies. Mushrooms release a lot of liquid. Then you just cook everything up.
It's easy and makes for very flavorful onions, without the oil!