At first I will smile. I'll try to stay calm and find a solution to the problem as best I can. If I am in the wrong, I will take responsibility, apologize and make amends. If the customer or colleagues is in the wrong, I will gently explain and apologize for the miscommunication or misunderstanding, and let them are appreciated.
When tempers become heated, I step back, I may ask the other party to table the disagreement while we both consider equitable solutions, or consult a supervisor in private for clarification and guidance. I can work rationally and reasonably with the other party to listen to one another, debate the issue and resolve our differences in a mutually-acceptable manner.