In a word, all you have to do is validate to get somewhere when you're arguing. I am offering here the 411 on validation. The word 'validation' gets thrown around like a beach ball in the summer, but it's important that you understand what it means. Quite simply, it's another word for 'listening.'
Sometimes we over-think things and make them more complicated than necessary. In an argument or disagreement, you must show the other person you are listening to what he or she is saying. This doesn't mean that you have to agree with it, but you must listen if you want to maintain any kind of working relationship with that person later.
Too often, people get heated in an argument and it turns into a power struggle that everyone wants to win. Say "see ya" to this adolescent wish and move on to the more adult compromise - flexibility.
The next time you have an argument with someone, validate that person's feelings simply by listening. Hear them out and you will find that they can move on a little more quickly. In addition, you will find that person become a little less angry and frustrated, and this, in turn, will help you to step down from your own anger stance. Practice makes perfect, so make an extra effort to listen the next time you're in the middle of a heated spat.