• Start by slicing your onions.  They can be thicker or thinner, it's just important that they're a uniform size so they cook evenly. 
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• Heat a large saute pan over medium high heat.  You'll want a pan large enough that your onions can spread out and have contact with the bottom of the pan.  I like to use a combo of butter and olive oil.  I use about 1/2 - 1 tablespoon (of butter and olive oil combined) per onion. Add the butter and oil to the pan and let the butter melt.  It should melt and sizzle a bit, but you don't want your butter to brown so if that happens, your pan is too hot.
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• Add your sliced onions and toss them around so they're all nicely coated with the oil/butter mixture.  They should sizzle a bit.
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At this point you may want to turn your pan down a little.  The trick to caramelizing onions is doing it low and slow.  It definitely takes patience.  You don't want them to burn or get brown right off the bat.  I add a sprinkle of kosher salt at this point.  The onions should slowly soften.  This is after about 5-10 minutes:

You need to stir them every few minutes so they cook evenly and don't burn.  After 10-20 minutes they should be quite soft and starting to become golden.  Add extra butter or oil as you go if needed so they aren't sticking to the bottom of the pan:

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• After 20-30 the brown color increases, but don't stop yet!  I think sometimes people stop too early.  you want them to be a rich amber color, these ones below aren't ready yet.  If you want to enhance the sweetness even more, add a little sprinkle of sugar at this point.  Either brown or white will work and it does wonders for the flavor!
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• This is more like it.  And I could have even cooked these for a bit longer if I wasn't so impatient.  They should be incredibly soft, sweet, and golden brown.  Also, they should taste amazing. Check, check, and check.
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