How to connect two users directly in realtime on a website?

I am trying to develop a web application that has to connect two random people.

The webpage has a form with many text boxes. My application requires two connected users to enter values in the alternate textboxes (so 1 of the user enters values on 6 textboxes if there are 12). And it has to display the results after a button has been clicked.

What should I use to connect two users directly? I am most comfortable with PHP, so it is possible to build this application using it? What other knowledge do I need to have?