Be courteous but firm. Know your policies, look at what you can and cannot do for the customer in order to work effectively and quickly.
Remember the customer’s perspective- put yourself in their shoes, what is it exactly that allowed them to become upset? Is it something out of your control, or something you can work on?
Sincerely apologize with an empathetic tone; if you sound robotic in your apology, the customer may very quickly become more upset.
Offer solutions. If in the moment you’re unable to find an immediate solution, advise the customer of your intentions on finding one so they are aware you are trying your best to assist them.
If the situation becomes difficult, have a manager or supervisor step in. Having authority assist in the situation will help provide better service to the customer and help the customer to realize they are receiving the highest level of assistance.