If an angry customer contact you, how do you deal with him?

 The very first thing you should do is find out what went wrong and why. 
Put yourself in your customer's shoes and consider what could be said or done to remedy the situation from their point of view.
Take responsibility for the actions of your company Do not place the blame on specific employees. 
Don't deny that a mistake was made, especially when there is clear evidence Admit your mistake.
you must admit your mistake before you can move ahead and start to make amends.
Don't be so afraid to take this step Apologize for the mistake.
simply saying you're sorry is often the best way to get a business relationship back on track.
Ensure the customer that it will never happen again.
After you have taken responsibility for the mistake and apologized in a sincere and professional manner, you must then start the process of rebuilding the trust that was lost Promising that such a mistake will not happen again is a good way to start.
Compensate the customer for his loss.
Even if your mistake didn't cost the customer he will appreciate an offer of compensation.
This can be something as simple as a lunch on you or a discount on his next order

Deal with the customer on the basis that there nothing personal with him.
also try hard to understand the cause of his anger and showed his interest in solving his problem.