I ate and learned to cook carnitas in Calif. But the best carnitas I've had were in Michoacan. There, hunks of pork were browned a little in lard, then water, a squeeze of o.j., orange rind, garlic, onion, cinnamon, bay leaves, and oregano were added. When the pork was cooked it was broken up a bit more, the other soilds were removed and the heat was raised so that the liquids would evaporate and the pork would crisp in the remaining fat. It was very, very, good. A few days later I had carnitas again in San Luis Potosi, though this time white wine replaced the o.j. Wonderful.
On edit: I had carnitas cooked in lard only in Calif and in Mexico. But those two times opened another door for me. I adapted my approach accordingly--they were too good. After a while I added an oven-finish option that I'd read in many recipes; convenient for the times you can't attend the pot on the stove, but I much prefer the stovetop start to finish.