How would you deal with an angry client/customer?

First of all, never blaim anything on a customer / client directly. If she / he got angry on any reason, try your level best to offer her / him for giving a place to sit. Then serve a glass of water. While they are drinking water, don't try to talk with them. When they finished drinking, then try to take them in confidence. And during this time keep your face smiling. Because your angry face can make them more angried. 

If your customers/  clients are on the distance, try to talk on phone in polite way. Although you were not committed any mistake, just take it on your own shoulders. And fullfill their losses or clear their problems for becoming angry. 

And it is said that " Customer is always Right "

Always try your level best to win their confidence. 

Always working in a customer service industry,we have to keep in mind that customer is the king and we are the face of our organisation.So we have to be calm and understand the problem of the customer by listening carefully to their problem.Never argue back or loose patience.Patiently listen to the issue and diplomatically try to find a solution for the problem and when you are calm and when the customer notice that his problem is aknowledged,gradually the situation will cool down and a happy customer will walk out!

never blame the client/customer or try to explain rushly before calming them and reassuring them that you understand what they are saying and take it upon yourself to fall for the blame.

apologize , promptly look for a solution and keep smiling to ease their aggitation and anger at the end of the day the client will walk out satisfied. (Customer is always right!)

First thing to is keep calm, actively listen, actively sympathize, apologize even if he/she is wrong or right (remember customer is always right), Look for a solution and everything will go smoothly as it is.