If you can find fresh or frozen, roasted Hatch green chiles, they are absolutely the best for this soup. But, I've made it with canned green chiles as well and it is still very good.
This soup starts like so many good soups: butter, onions, carrots, celery, and garlic. Plus, the green chiles obviously!
Add your cubed potatoes along with a little flour to thicken the soup.
Add stock and simmer until the potatoes are tender. Then turn heat way down before adding milk so it doesn't curdle.
Use an immersion blender or traditional blender to blend soup until it's smooth. Some chunks are good in my opinion for a little texture to the soup.