One of the best ways to help make unhappy customers feel better about your business is to listen. This shows that you care about your customers, and are looking out for them.
Employees receiving customer complaints should always be friendly, polite, and helpful; and try their best to resolve the problem if they can. Even if a problem cannot be totally solved, the fact that your business did everything you could to help will make the customer feel much less negative about your business, hopefully enough to keep them with you (so you can ensure they are fully satisfied next time around!).
Sometimes it can be difficult for an employee to feel like helping an angry customer, particularly if the problem is not their fault; however it is crucial that they remain polite and helpful at all times.
Remember that body language is a large part of communication, so listening while looking away will just make the customer think you are ignoring them. See the links section for further information on Body Language.