Acknowledge, Question, Understand, Answer. In that order, and the order is the whole thing.
A service-recovery framework used widely in coaching and client management; no single originator.
Four steps for the conversation you least want to have. Most people go straight to the fourth, which is why complaints escalate.
Acknowledge. *"I'm sorry to hear you're feeling this way. We are committed to resolving the issue you're having."* Not an admission of fault — an acknowledgement that they are unhappy, which is simply true.
Question. *"When did this issue first arise? What specific examples can you give us?"* You cannot fix what you have not defined, and the questions themselves demonstrate that you are taking it seriously.
Understand. Paraphrase it back. *"If I'm understanding you correctly you're feeling… as a result of… Have I got that right?"* If the answer is no, go back to questions. This step is skipped almost universally and it is the one that defuses things.
Answer or action. *"What actions do you think we should both take from here?"* Agree a way forward, then set a time to check it is actually resolved.
Jumping to the answer is the instinct, because it feels efficient and it ends the discomfort. It also tells the person you were not listening, and now they have two complaints.