I make eye contact, smile, nod, and give all the proper social cues when dealing with people. However, they're all driven by conscious effort and not instinct. I can forget to do them when I'm distracted or engrossed in a problem.
I can do public speaking.
I can quickly learn someone's speech/intelligence level and talk to them at their level (provided they're not above my level, of course). I can also communicate with people from any profession and quickly learn their professional lingo. For a while, I was the liaison between our engineering and legal departments, and would 'translate' between them. I often get called on to explain technical issues to non-technical people - I've had to present stuff to politicians, regulators, lawyers, and executives (executives are the hardest to get through to, because they always want the shortest explanation possible to make a decision and move on). When I met with the counselor who diagnosed me, I learned all the psychological terminology I could - it's all about precise, accurate communication for me.
I've learned to "reverse-engineer" people by observing their behaviors, actions, and reactions, and deriving their worldview and motivations. This helps me know how to deal with the person. I use this to pass for a real understanding of people. When I am working with someone, I'm constantly running flowcharts in my head to answer "What will put this person at ease? What will help this person to know I'm on their side? He seems proud of what he did - I'd better compliment him on it. How can I lead him to this solution without forcing it on him? Let's discuss the requirements, pros and cons, first and see if he gets there on his own - I don't need credit for the solution, I just need the solution to work."
It takes some time to observe and analyse a single person, but I'm grateful that this approach works for me because it's the best I can do. My wife is a quick and accurate judge of character and can read emotions from the smallest cues - it's like magic to watch.