Identify the problem
First, identify the problem on why the customer is angry. There may be a host of reasons to this problem. Either the customer is not satisfied with the service or the quality is not up to the mark. Identifying the problem may be a difficult task for you if the customer is yelling but always try to be patient and attempt to make amends.
You must be attentive while listening to the customer because if you are not, it may further irritate him or her. Talk in a volume that is not very high and do not argue with the customer even if you are not on the wrong side or if someone else is responsible.
Find out a solution
Try to find a solution to the problem. Always agree to things that you can do if you and do not make false promises as this will further agitate the customer.
Deliver on the promise you have made
You must be worthy of your word to the customer and the problem should be solved in a timely manner. If things are done perfectly and in the time you have asked for, you may end up with a satisfied customer and hopefully your job.