Can you give me a good example of handling angry customers through the phone?

Actively listen. Let the angry client talk through their problems and get it all out of their system. As they talk make indications that you are listening such as "uh huh", "really?", etc.. This step is important because the more time a customer spends airing their grievances, the more time they have to calm down.

1. Allow the client to express their opinions. Allow them to communicate their feelings however they choose to without passing judgement. Step in only if the client becomes directly abusive towards you.  
2. Maintain your personal integrity at all times. If the customer is abusive, calmly interject something to the effect of "I appreciate your frustration with the situation however attacking me will not improve anything - I would like to help you."  
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4. Be sympathetic. Make sure the customer knows that you understand their frustration and acknowledge any mistakes that have been made. Recognize the customer's feelings about the mistakes - that is, how it must have felt to be the customer in this situation.  
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6. Be empathetic. When appropriate, show empathy. Empathy implies that you feel the same way as the customer and truly understand their feelings. It can create further issues to say "I understand your anger" if you do not truly understand, as the customer may shoot back "You have no idea!". Using a phrase like "I can imagine how upsetting that must have been" is a better way to phrase this.    
7. 1. Ask questions. After they complete their story, ask about the facts and details of the matter at hand.  
   2. Move into solution-mode - know when to ask open-ended questions, and when to stick with "yes" or "no" questions.  
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   4. Apologize when appropriate. Apologies can often be interpreted as an admittance of guilt. There are three types of apologies that can be employed in these situations, choose the most appropriate:
      • Direct: "I apologize that we did not send your order on time."
      • Blameless: "I apologize for the fact you are frustrated - let's see if we cannot turn this around."
      • Fake: "It sounds like we owe you an apology."
        • Many customers interpret this to be an apology when in fact none is ever made.
        • Offer to try to fix the problem. Never promise to outright fix the issue, but always promise to try. If you make an attempt and fail, it will create further issues if you promised total resolution.  
        • Gain agreement on your resolution. Make sure your client understands what has been done at the end of the call. Even if the issue is not totally resolved, gain agreement on the resolution that was reached.
          • Example 1 (total resolution): "So just to confirm, I have walked you though reinstalling your application and now everything works - correct?"
          • Example 2 (pending resolution): "So just to confirm, we have decided that your toaster is in need of a repair under warranty and I am sending you a box for you to ship it back to us - correct?" 
          • Write a clear, concise log of the incident. Document (in detail) every major point of the call. It is not important to note every single word uttered, but keep a point-form log of anything that may assist others who deal with the customer in the future.