We all want our feelings and thoughts to be heard, valued and understood. Listen for understanding. Rephrase what you have heard your partner say and then ask if this is correct. Save your side of the discussion until you have validated your partner's feelings. Validating your partner's feelings and thoughts is the key to success.
Blame fuels the fire of disagreement.
Most of the time we believe that our position is acceptable and tend to blame the other person for any misunderstanding rather than to see our own flaws in communicating. Analyze your part in fueling a problem and avoid blaming others. Be responsible for your role in the relationship. We tend to learn by example. If your parents were poor communicators more than likely you have learned and now act out some ineffective ways of communicating.