Caramelized Onions

Determine how many onions you will need. Caramelizing reduces the mass of the onions a lot so even if you start out with a pan full of raw onion, they will cook down substantially. For most purposes, one onion per person serves as a good rule of thumb. 

Find a large, heavy skillet. A heavy non-stick or well-seasoned iron skillet is best. 

Get sweet yellow or white onions. After cleaning the onion of the dry skin and the root and stem tips, cut the onion in half, top to bottom. Then slice the onion flat side down to make thin strips of onion. Make sure to separate the layers. 
Pour enough pure olive oil to coat the bottom of the skillet plus about a tablespoon more. Heat the skillet on high until the oil is very hot but not smoking. 

Add the onions all at once and reduce the heat to medium high. Don't worry if the onions are piled high in the skillet. They will cook down. (Note: some chefs prefer to caramelize the onions in small batches (thin layer), so the onions caramelize, rather than steam.) 

Using a spatula, turn (toss) the onions so that all the pieces get some oil on them. 

Continue to turn the onions with the spatula about every 8 to 10 minutes. If some of the onion appears to be burning, move the onions to the side and add more oil (one or two tablespoons at a time) and stir the onions into the fresh oil. 

Continue to toss the onion with the spatula until all the onion slices have reached a dark, rich brown color. After 25 to 30 minutes, the onion will be well on the way to browning. This is the sugar in the onion caramelizing. 

Remove the onions, turn off the heat and add a little water or white wine to the pan to deglaze it and get the delicious dark brown glaze that has cooked to the pan. Use only a little liquid, no more than 3 to 4 tablespoons, to deglaze. Then stir the resulting glaze into the onions.