What would you do if an Irate customer or client doesn't want to listen to any of your explanation? How can you make him/her listen to you?

Listen very carefully,you need all the words and or deviations they make in their chattering,ranting and raving.Don't attempt to stop them,it worsens an already messy situation,let their fuel tank get to zero on the reading meter and then take them back slowly bringing their concerns to the fore and how unmanageable such a scenario would be.Don't blame them,see things from their angle by giving them your shoes.

we talk about everything expect the business, i try to make customer happy and talk about something not related t oour business

Empathize, let them know that you appreciate they are upset. - Build rapport fast - Use their language and some of their mannerisms if you are face to face.

Solicit feedback. Please let me help you. explain to me the problem in detail.

Apologize, it's ok to apologize to the client for the inconvenience. - Don't say you are sorry, but apologize.

Take ownership and formulate a solution

Follow up. ask if you could have some time to work on the problem.

Be patient. An irritated customer won't be placated by anything but a satisfactory resolution to their problem. Getting angry back at them won't help.

Approach the angry customer and ask what they are displeased with. Usually restating the issue they are having will help to calm them. For example, say, "I can understand your frustration with..."

If they ask for the manager, get him/her quickly and do your best to solve the problem.

After they address the problem, apologize for taking their time and inform them that you will do everything possible to correct it. Then, make sure you do everything possible to correct the situation.

Compliment them after the discussion. Say something to the effect of, "It's people like you that help our business."

The next time they call back, ask how their day is and do everything possible to be polite.

Don't rise to the occasion , if they are getting really angry you could ask them to leave the store or go and get someone higher than you.

What I am doing:

I will offer a cup of water or tea or drink and will talk about him or else not specific about the business line.

then,

slowly slowly I will brigh his or her attention to the specific point and will try to find the middle way or most of the times I will do the same which my position allows me.

Depends on the situation, if its by phone let customer talk first, note down the matter and then apologize for the inconvenience you have caused to the customer then discuss resolutions, before ending up the call make a summary of what you have promised  and make follow-up call if service was restored, whilst if situation is on the customer premises same situations can be applied but this time make them feel that you understand their problem and if you can resolve it alone then do it otherwise give them assurance that the issue will be resolve on X amount of hours or days.

The best thing to do is to listen to their needs. In most cases, customers will calm down once they have realized you are understanding their problem. If they are still irate, you can ask them what, according to them, is the best solution. If nothing else, give the customer what they want or put them in contact with your immediate supervisor.

You should listen to him first and understand his pain and consider it as if it is your pain.

Tell him i understand your pain and you are right100% and confirm whatever he said even if you do not like. Then start directing him from that point.