Sometimes, things can get a bit of a hot mess. Whether it is your own fault or just circumstances, clients can sometimes take their issues out on you.
Don’t take it personally. We all make mistakes and it is what we do to try and fix the situation that is more important.
Empathy. Empathize with the customer. “I can see how that would upset you. I would feel upset about it as well.”
If it is something that you have done, own it. "I apologize that this has happened.”
Give them guidance and assurance. Let them know your plan to fix the situation or work around whatever has happened so that things can get done.
If it escalates further, after completing those three steps, let them know that your manager will give them a call to further discuss the situation. And then let your manager know.