Alright here's the basic really homey white posole, which you can very easily make into the more common red version.
2 tbs. canola oil
1 lb. pork butt or shoulder, trimmed of fat and cut into chunks
2 cloves garlic
1 med. onion, chopped
1 15oz. can hominy
4 cups chicken broth
salt to taste
1/2 cup chopped white onion
limes cut into quarters
dried oregano, to taste
1 or more (more's good) ground or crumbled New Mexico or Guajillo chiles
thinly sliced radishes
1/4 shredded lettuce or cabbage
Heat the oil in a dutch oven or a heavy pot. Add pork, onions, and garlic and fry that over medium high heat. Once the pork starts to get crispy, about half an hours time, add the drained hominy and the broth. Season to taste with the salt, bring it up to a low bubbling boil, then reduce to a simmer and let it go another half hour, partially covered. Serve and add the garnishes to your taste; goes great with hot corn tortillas.
To make the red version, just add one or more tablespoons of ground ancho, guajillo, or cascabel chiles to the posole while it's simmering. this one's my fave!