To come back to the How, you really cant teach something. You're just able to show your interest and involvement in some topics and thats a keypoint too.
Thank you for the thoughtful questions. It seems to me, that in this kind of class, there are things that anthropology has worked in a way other disciplines have not.
The first, of course, is the concept of culture. I do not mean by this an extended theoretical discussion of the concept, but the basic fundamental awareness of culture and its impact. My students seem to feel that their thoughts and behaviors come entirely (this is an exaggeration) from their own individual choices and personality. Through the process of comparison with other cultures they gradually discover how they too are caught in the web. This, of course, raises issues of agency. The encounter with cultures different than their own is also important. Many students today are willing to accept the differences between cultures, but they do it with an attitude of "that's their culture, so its cool and it really doesn't have anything to do with me." Anthropology courses can force the students to really see differences and then to begin, hopefully, to understand them, to see that a way of life that is very different from our own also has meaning, even logic to it. Sometimes, the way others do things may even seem superior or beautiful. Again, of course, this then reflects back on one's own culture which begins to be seen as a choice out of many alternatives rather than the only reasonable way to do things. I think these are all important lessons, and they are ones that come out of our courses more strongly than elsewhere. For me, the specific material of the course is secondary to these general concerns.
The other matter, however, that we can offer is a type of method which they will not experience in many other courses (perhaps sociology). We can have our students directly gather primary cultural data from live human beings though interview, observation or other methods. We can then have them try to analyze the data they gathered. I have had students from my "Fieldwork" course report to me that their fieldwork project was one of the few things they really remembered from college years later. Based on this, I personally, am trying to think of ways to get students "doing" anthropology in as many of my classes as possible. Figuring this out is taking some real effort, and I think it will increase the grading load while reducing course content, but I am pretty sure it will be worthwhile.
PS -- apologies to those of you who are not assuming that this is a cultural anthro class. Its about all I teach.