If you want to be a good communicator and also a good persuader you will need to learn to not try too hard! That is surely counter intuitive. If people sense that you are trying to hard to persuade them they may resist you says Kurt Mortenson in his book; “Maximum Influence”. People need a reason to trust you before they will accept what you are saying. Listening builds trust.
In order to listen well you will need to get comfortable with the silent spots in a conversation. When someone stops talking you will need to develop the discipline to keep quiet and be patient long enough for them to start speaking. I once had a boss who was a master at this. It is unbelievable what you would wind up telling him just because he went silent. People will open up to you if you create the conditions for that to happen. When you learn from them what they are most interested in or concerned about then you will be able to give them a targeted response. This much more effective and persuasive than presenting a laundry list of things that you hope will win them over.
Introverts tend to listen more than they speak. That is because they need to think about their statement and responses. Studies have even shown that introverts often out persuade extroverts because they ask more questions and are inclined to listen more.
Try to listen more for the next week and then just see the results for yourself. It only takes a few weeks to develop a new and better habit.