In my opinion, before you ask how to be a good communicator, you should first ask how to be a good listener. Every good communicator is, first and foremost, a good listener. So learn to listen, and absorb, what the other person is saying. Being attentive gives your audience the correct impression that you are truly interested in what he or she is saying. Aside from having the chance to really understand their point, acute listening also builds trust between the two of you. It is or course easier to communicate with the people we trust.
Being a good listener also help you absorb every point made by the other person. That will be a good place to start if later in your conversation you will need to rebut their argument using their own words. Though you don’t want to get into an argument, it is sometimes necessary to stress your point. And listening can greatly help you with that.