If you follow this recipe, you will get very close to the carnitas actually served in Michoacan, Mexico, and in the many Michoacano restaurants across America.
Cut the meat into large chunks, or leave it on the bone if the hunks will fit in the pot you are using. Salt them well.
Fill your pot with the lard and heat it to about 200°F or thereabouts. You might need more than 3 quarts. Remember, you will be able to reuse this lard later, and almost all of it will stay in the pot, so fear not.
When the lard hits temperature, add the pork. Now, there is an order to things. Different pieces cook at different rates. Longest cooking bits, in order, are: hocks, feet, tongue, heart, jowls, shoulder, ribs, hind leg, skin, belly, loins. Depending on what you are using, add the longest cooking bits in first. In general, wait 30 minutes before you put in the next item. Even loin will ultimately need 1 hour, though, so keep this in mind. Carnitas is a process.
Once you put in the first pork item, add all the remaining ingredients and let things cook at about 195°F, more or less, until all the various piggy bits are soft and tender. Normally this takes about 4 hours, but could be more with wild hogs.
When the meat is starting to fall off the bone, remove it from the lard and let it cool a bit. Carefully debone it. If you are using feet, this will be fiddly. Now, you have two choices. If you don't care about reusing the oil, heat it to 350°F and fry the pork until the exterior is crispy. If you do want to reuse the lard, remove all but about 1 cup and then sear the pork bits in that lard until crispy.
Chop and shred the meat as you like and serve. It will keep a week in the fridge and freezes well.
Notes
Some Keys to Success
Use various cuts of pork. This is a fun place to get adventurous, because it will all get chopped up anyway.
Use fresh lard, and lots of it. Remember you can reuse it and you're not actually eating all of it.
Be patient. This is more like confit, as in slow cooking. Your patience will be rewarded.
Do make lots. Carnitas is a process, so you want to make a big batch and then eat off it, or freeze it, for easy dinners later.