Be respectful, even with upset customers.
Customer service is not an easy job. Sometimes your customers will be angry with you, need extra attention to understand things and sometimes things will simply be difficult.
The worst thing you can do in these situations is lose your cool. Be kind, sincere, respectful, understanding, remain calm and professional.
A great piece of advice I have heard that applies to all areas in life is:
"Treat every person that you meet as if they are the most important person with whom you will speak that day."
After your customer vents, they want to know that you understand where they are coming from and how they feel. Show sympathy for their situation and express empathy for their frustration to recognize the fact that they are frustrated. By keeping your composure, you may find that your customer will calm down as well.
Respect and understanding go a long way toward smoothing things over.