Interesting question! I believe it's possible to teach "common sense", the kicker is whether or not the person you are trying to teach it to is willing/wanting to learn it. How would I teach it? First, determine the context where the term "common sense" is being used. Then teach it the same way you teach any other subject, break it down into sections.
So many people believe "common sense" is something that if you don't possess, you're screwed, which is not true. It can be taught and learned like any other subject, and like a lot of things, it takes practice. Its just some people will have a better knack for it then others in certain areas of life. "Common sense" is just a tool that people can learn to apply to any part of their lives. Well, at least thats my perception of it at this moment in time, which (these days) can change at any moment.
Have you ever had a negative vision about another persons life? If so, what did you do with the information?