Listen without interrupting. Show that you understand how they feel as well as what they are saying.
Analyse the problem. Differentiate between facts (the report has three errors in it); assumptions (it was clearly done at the last minute); generalities (your junior people aren't up to it); and emotions (I feel let down).
Work out the reason behind their rage. Is it because their boss is angry with them; because no-one from your organisation is listening to their concerns; or because they feel that a promise you made has been broken?
Stay very calm. One highly emotional person is more than enough.
Respond quickly. See if there is anything that can be done immediately to make things better. If so, focus on this rather than the cause of past issues.
Find out what actually happened. Dig deep for the facts about what the sequence of events was and avoid placing blame (or you'll find it harder to get to the truth).
Take full responsibility for finding a solution. See things through to full resolution and keep communicating with the client - knowing that a senior person is dealing with their concerns will soothe all but the most irate.
Never view the client as a lost cause. Great client recovery often leads to stronger and deeper relationships than those with consistently happy customers. And you don't want them bad-mouthing you or your organisation.
Take preventive measures. Let them know what you have done to stop the problem recurring. Clients will feel that their pain was more justified if they have had a positive impact on your business and stopped others having to go through similar angst.