First I always allow the customer the space to say what they need to say, and explain to me fully why they are upset. I ask them to give me the details of why and I will see if its something I can solve, and if not I promise I will do what I can to help them find a resolution. I take ownership of the situation if something was done wrong and I apologize for the inconvenience or for what happened. Often times I have found a customer just does not understand a process or are not in the right area so I take the time to show/explain to them where it is for the future as well.
Usually once they have the chance to vent it out and you make sure they know you are eager and willing to help them in whatever capacity you can it tends to be a lot better of a conversation moving forward.
This article has some really helpful tips: https://www.wikihow.com/Deal-With-Rude-Customers
Unfortunately, this is a part of most jobs. While you may not always deal with customer's there are always rude people.
When I am dealing with someone who is rude, I take all emotion out of the situation. Sometimes the person has just had a bad day and they are venting to you. Not that this is acceptable, but it does happen. Remember, while you are working, you are the professional and you have to handle the situation. Simply be respectful to the person, answer their questions and try not to take it personally. It's probably not directed at you.
If the rude customer becomes more agitated, all you can do is try to resolve the situation. As a worker, you need to make sure the customer is getting what the came for. Listen to what they are saying and offer solutions that you can provide. Sometimes people just want to be heard, understood and have someone help them. Do all of this why being polite. If you give the rudeness back to them, that makes for a very bad situation.
If the customer is not listening to you or is not happy with your solutions, the only thing that you can do is escalate that to your supervisor and have them handle the situation.
If the situation becomes personal or offensive, you DO NOT ever have to tolerate that in a customer service position. You should remove yourself from the situation and immediately get your supervisor. Everyone deserves respect.
As you are dealing with them, remember that it is generally them who have the problem. Don't let them ruin your day (easier said than done) because then they win.
Hopefully this doesn't happen to often for you!
First I have to agree with Chelsie that letting the customer vent is a great way to deal with a rude customer. Sometimes the customer has come to where you work with a particular expectation and they become upset when that expectation can't be met. (Like getting a last minute gift or getting a discount that they saw online but the item is sold out.) They may begin rude, like yelling "That's unacceptable!" or something less polite. But this is the point where you have an opportunity. Instead of saying something like, that's how it is, attempt to learn more. So instead of addressing the rude comment, address their unmet need. "I am sorry that we do not have X. Is there something else that I can help you find ?" That is where the venting comes in. They will often begin to explain the source of their rudeness. "No, my mom really wanted this thing and it is the only thing that she asked me for. I really need to find it." So this response gives you options to act, instead of becoming angry yourself. And often venting gives the person time to work through the emotion that they are feeling. It is hard for most people to maintain anger or aggression for longer than a few minutes. So in the situation that I mentioned, you may have the option to call another store to see if the item is available. Even if you don't find the item, I have found that customers are often remorseful about being rude and often understanding about the item not being available anywhere because you took the extra step to try and find it.
Another element that you need to consider is that the person isn't intending to be rude. I live in Texas where people are super nice and say things like "ma'am", "sweetie", "dear" and "honey" and say "please" a lot. I am not from Texas (originally from Nevada) and the familiarity of the language sets my blood to boiling even before I ask for what I want. I have said "I am not your sweetie" a time or two. Bring in someone from New York or Boston, and the situation can go downhill fast. They have little patience for the niceties of "how is your doing going?" type questions. They are direct and clear with what they want. In their home cities, they are not considered rude at all. You need to consider if what they are saying is rude or is it just how they are handling the situation that feels rude. So listen to the words as much as the tone of voice. Do not accept being called names or the use of bad language if it is offensive to you. However, someone saying, "You need to listen to me. I just want this" may not be meant to be rude at all. They may just be in a hurry.
I have found that handling an upset customer well can be very rewarding, both emotionally and financially. I have seen an initially rude customer buy more or leave a bigger tip because they have been handled with calm respect.