How to create a private chat application?

This is not possible with php alone. php is only executed on the server before the browser loads the page. Once the page processed and the data sent to the client (browser), there is no more php going on. So making a live-chat via php alone is not possible, unless you are okay with "refreshing" the website every time.

You could do it the way you want it with php and combine either Ajax or javascript to check in regular intervals if there is a new message to be displayed.

As for the database, it depends what you want to save. Obviously you'd need to save the actual message in the database, but anything else is up to you. If you want to save who sent a message and when it was sent, you'll need the appropriate table structure for that.

Yes, you can build real time applications with php. Take a look a the Ratchet library. here's a simple tutorial for you to get started: http://socketo.me/docs/hello-world

Thanks everyone for your valuable suggestions . Yes the user should be signed in and the chat would be saved in the database for later review by the user. Moreover, you can take the example of the facebook chat. I want similar to that.

Rohin, could you post some more information regarding the functionality of what you want to build. I.e does a user need to be signed in, will you be keeping chat logs? This will help us make recommendations. Also, Emmanuel Salom, recommended Ratchet for routing chat info between sites, but you could also use Node.js. Here is a good goggle group discussion comparing the two.