Looking for a simple tutorial for a private chat system

I have searched for tutorials or information about how to build a simple chat support system. Where I, the administrator, can talk privately with visitors on my website. One at the time. And visitors will not be able to talk to each other.

But I have not found any good information on how to make this the best way.

Do you know if there’s any easy tutorial for this? Or if you can describe and show how to do this in the simplest way. Just so I get the basic functionality of private chatting so I can develop the rest by my own.

I am programming in php, mysql and javascript.

Here is an image illustrating how I wish it to work.

Can you be more specific what parts I should read that addresses the most important things for what I need?