lately I started participate in toast masters meetings in my city. I am not sure, whether you mean this kind of communication like public speaking, but even after just one meeting I learnt a lot about how other people reads body language.
And because 80% of communication is not verbal, in most cases those kinds of details are very important too.
Lately I also started wondering about people which works as copy-writer. Nowadays those kinds of skills can be very helpful.
Communication skills is very broad term. A more specific sub-goal for me is to learn how to listen. To create and hone the ability to see things from other persons perspective and understand their position. That includes both verbal, nonverbal and reading-between-the-lines comprehension.
Another ability that goes hand in hand with the first is asking good questions.