Rinse and cut the pork shoulder into medium-sized chunks. Add it to a large pot with garlic cloves, water, salt, and lard. Cook on a medium flame while keeping the pot covered.
Lessen the flame to medium-low and cook until the pork is tender.
Reduce the water level on a high flame with the pot uncovered. When water content becomes low, pork will begin to fry in lard and fat.
Keep frying until the pork is crispy and brown. It will take 15 minutes.
Grate the pork with forks a little. Traditional style Carnitas De Puerco is ready. Serve it however you wish.
Modern Style
Sprinkle the salt over the pieces of pork and refrigerate it for 2 hours before cooking.
Preheat pork lard for ten minutes on medium-low heat in an oven.
Place the pork pieces on the tray containing lard with enough space between them. Cook on medium heat so that the lard keeps bubbling. Cook for half an hour and repeat the same for the other side after flipping.
Add all the remaining ingredients. Bring to a simmer and cook for another 90 minutes.
Dish out the pork pieces and grate with forks a little. Modern style Carnitas De Puerco is ready.