One of the key points of intercultural effectiveness is being able to change our behavior to suit the needs of the situation. In the cultural intelligence world we call this CQ Action.
One of the most common areas of adaptability has to do with eating and food. The process of eating can be a rich area of discovery for people and a great way to learn about a culture. In the US, eating and food is often looked at as just a means by which we get energy into our system. But in other parts of the world the process of eating together and the traditions wrapped up in food can have much more significance. So take the time to savor both the foods that are part of the new experience as well as the relationships that come along with it.
Sometimes developing our intercultural capacity can seem overwhelming. My advice is to take it one bite at a time.
Give a listen to this great article on NPR about the cuisine of Kazakhstan. http://www.npr.org/blogs/thesalt/2013/03/04/173448013/in-kazakhstan-no-horror-at-horse-meat