There is not one step or one practice that will do it, not without spending many years. You have to address different parts of the mind. There is the belief in being right, the point of view, the emotion, the feeing of needing to defend your argument against another part of the mind. If you address these different parts of the ego mind in a divide and conquer approach it can be done much faster.
In the audio program in self mastery I teach people the exercises and practices to dismantle the internal dialogue. The first audio sessions are pretty simple and are meant to help an individual build a foundation of consciousness for the later exercises. If you have been seriously practicing meditation for a while they may not engage you very much in the beginning, but the exercises and practices build on one another and become more involved. More at
Self Mastery
I learned this approach from my mentor, Miguel Ruiz, author of the Four Agreements. I developed into a system for dealing with the emotions and internal dialogue in the mind. It is possible to quiet the mind and feel peace and happiness. It will take some work. That is my experience.