What is the best way to handle most annoyed customers ?

Calm them down by listening to them,try to see things from their point of view and assure them that whatever happened was not meant to hurt them.An apology can work wonders.

The best you can do is to first of all take the customer as the boss. Take a step of believing what the customer is complaining about.Listen attentively, apologize for the mistake then ensure you satisfy the customer and never forget to say thank you to the customer for bringing the complain to your attention. All of this followed would create an everlasting moment for the customer hence always coming back for your services.

Annoy him too, by providing excellent customer service and solving the issues customer has faced.  

Listen to the customer... keep calm and offer a solution to the problem

First of all  if you are the cause for the annoyance,offer sinciere apologies,then try & COOL THEIR HEELS & ensure you make them happy at the earliest