The major issue with "having-a-chat" with a customer is that many developers are simply not listening. Seriously, that a big issue.
A customer has only one thing in mind: "I am right!"... You know what? He's right most of the time. He (or she) may lack the technical knowledge, may have missed the obvious documentation, may be asking for the impossible. A mad customer often means that something is wrong...
The first thing you should do is listen, don't argue. Even if the request does not make any sense, your customer is simply trying to explain issues that you may have missed. Shut up and listen! Take notes as it will show that you care. Look at him, right in the eyes, not at your laptop. Let him do the talk and keep calm.
After a few minutes (of a few hours...), once he'll feel that you have listened, he'll be prepared to hear you talk. Start by repeating what you have understood of the issues, to make sure that you got it the right way. Propose to investigate and do some analysis before promising to fix it by tomorrow. Never, I mean really never make a statement that could be wrong if something goes bad. False promises are the worst in customer management.
Sometimes a quick hack will give you more time to investigate. Make sure that the customer has understood that this solution is temporary until you find the real source of the issue.
Dates are gold! Plan some dated milestones if solving the issues can take more than a few days. Ensure frequent updates to keep him informed of the situation even if nothing has changed or improved. Your customer won't feel that you've put him on a waiting list, to be forgotten.
When investigating, involve your customer in the process as he may give you critical informations that are not obvious by looking at log files.
On a new feature request, try to see beyond the horizon as your customer may be asking for a workaround, hiding the real issue. Listen to him, let him explain how it should be done in his business. Learn how to do his work his way before trying to improve a process that you may not fully understand.
Never put the blame on somebody else or another team. You are the one representing your company thus you are the company. There is nothing personal in there, it just business. Take any critics as being targeted to the company, not yourself. Sometimes it's not easy, but that how you will look professional.
Remember that all you know is what the customer has shared with you. The more he shares, the more you'll understand. A mad customer is a gold mine of informations. A happy customer will only say: That's cool...
Listen! Just listen! There is a good chance that you'll better understand how it should be done...