A couple of hints. One is that I think the easiest way to start doing this is to practice active listening, which is just saying back to the other person the main ideas and feelings they are expressing. This a simple rule, though it can be hard to follow. Active listening forces you to pay attention, and it shows the other person you are understanding, plus if you get something wrong they can correct you.
The other is that when you are arguing disagreeing with someone and they won't listen to you, try listening to them until they feel understood, and they will probably be more interesting in listening to you. Or perhaps the two of you could first reach an agreement that both of you will listen to the other until they feel understood, and then decide which of you will be the first talker.