The art of reading faces is ancient and comes from the subconscious and biological need to understand each other. Animals and humans have the same ability to read body language and get impressions of another's intentions. Learning how to understand those cues and use them in negotiations creates advantages the opposing side may not have. Conceptually blending the information makes additional clarity on which pathways to use to achieve goals.
Imagine if you were able to understand what a person was thinking without actually having any magical ability to do so. If knew what they wanted and understood their environment you may be able to reasonably get an impression of their thinking. It isn't always correct but you can be accurate enough to test their thinking with your own words and comments.
Consider the environment and context of the facial expressions first. Look at what they are doing, what people are talking about, where their focus is, and under what circumstance they are participating. You should be able to get a better impression of the forces and factors on each person in the room.
View their facial expressions and try to determine what they mean. Is the person's facial expressions positive, negative, joyful, upset, distracted, etc...? There are at least 21 facial expressions that we use to express our emotions. Emotions are based on the way in which we think about things.
Therefore, if you match the environment, behaviors, context and facial expressions together it is possible to determine the latent functions going on in the brain. The more you know a person the better off you are able to read their expressions because you have a context for their baseline behavior. Changes mean something is going on.
Reading people is an important but not easily developed skill in negotiations. Understand what people say and why they say it makes a huge difference. People reveal information and understanding how that information fits with the negotiation can give you a tip off on what people are willing or not willing to accept. Negotiations is not only about having a position but also about finding out how to get the other side to agree to that position.