Learning how to caramelize onions should be on every home cook’s bucket list. Caramelized onions are an intensely flavorful ascension from the simple onion which gave it birth.
Cut off ends of onion, cut in half from root to tip, and proceed to slice from root to tip in ¼" cuts.
Melt butter and/or oil in saute pan on medium heat.
Add onion and toss to coat completely in butter.
Let saute for thirty minutes, stirring occasionally. Don't stir too often or the onions won't brown quickly. Stir when they are starting to brown, but not burning. Be sure to scrap fond off the bottom of the pan as well when stirring to incorporate it into the onions.
Once onions begin to turn brown you may need to drop the heat to low to prevent burning and ensure even caramelization.
When the onions are caramelized to your liking, deglaze the fond with water (or wine or balsamic vinegar for more flavor) and stir into the onions.
Let liquid evaporate and remove the caramelized onions from the pan.
Notes
Using only butter works, but can cause the onions to burn more easily. I typically add half butter and half oil.