Knowing how to caramelize onions correctly should be in every cook's repertoire. The basics are low to medium heat, not too much fat and time. Oh, and onions, lots of them. Onions cook down quite a bit. In the photos, you see that four cups of cut onions makes about one cup of caramelized goodness.
There are many other ingredients you can add to or after the caramelization process, sugar is the most popular, although onions have enough of their own to brown properly.
One teaspoon per onion can be added, however, to deepen the brown color.
Slice onions in rings or vertical strips and heat some oil or oil-butter in a pan, one to two tablespoons per onion or cup of sliced onion. Pour all the onions you cut and start cooking, stirring every few minutes. Be sure to keep the heat low. High heat will burn the sugars and make the onions bitter. They will turn a dark brown color in 40-60 minutes. They are done when they turn as brown as you like them. Some people like golden brown, some like mahogany brown.
You may deglaze the pan with a little water, vinegar or alcohol, depending on what you want in the end. Deglazing makes them a bit softer and they begin to lose their shape. Adding a little butter at the very end or a teaspoon of soy sauce will enhance the flavors in different directions. There are also many herbs that go well with caramelized onions. Try thyme, rosemary, salt, pepper or paprika powder.
The best onion to use for this project is the basic yellow onion usually found in the grocery store. White onions will also work. Sweet onions would seem like a good option but are best for short cooking times or raw eating. Red onions can be caramelized and have an interesting color, but the yellow onion is king.