3-4 pounds fatty pork. I use boneless country style ribs. In her recipe for carnitas, Diane Kennedy recommends pork shoulder, bone removed. The upshot? You want a nicely fatty piece of pork, bone removed.
6 cloves to 1 bulb garlic, peeled
tomato paste, about a tablespoon
1) Chop the pork into pieces of a size you'll be happy with in a taco. I usually go with roughly 1/2" cubes. If there are enormous veins of fat, cut them off and throw them away (or save them for another use, if you have one. I don't.), but don't worry about removing all fat; you bought a fatty cut for a reason. The cubes will shrink some (and eventually shred, depending how long they're on the stove) during cooking.
2) Put the pork into a large saute pan (nonstick will be easier to clean but will not produce the optimal results) with the garlic cloves and salt. Put cold water on the pork and garlic until they are just barely covered, set on burner, to high or medium-high and bring to a boil. Turn the heat down so that it is boiling briskly but not boiling over.
3) When it comes to a boil, add the tomato paste and stir it in. Cook for the next 90-120 minutes or so at a brisk simmer, checking in every now and then to give a stir (sometimes it's more, sometimes it's less, but I find it's usually at least 90 minutes).
4) Let all of the water boil away. The carnitas will begin to stick to the pan. Add about 1/4 cup of water, and scrape away at the bottom of the pan so that the brownings on the bottom get stirred back into the mix. I use a wooden spatula to do this. Let the water cook away again. The carnitas are technically ready. However, if I said 90 minutes, you budgeted 90 minutes, and it has now cooked up in... 70, with dinner guests not even arrived, just add more water, 1/4 to 1/2 cup at a time, and let it cook down while you finish preparing other stuff. Scrape diligently at the bottom of the pan when you add the water, getting all the browned and stuck-to-the-bottom stuff up and stirred in.
5) serve as you choose, but I like it with the sides as described above, and warm flour tortillas.