The most common way to engage in real-time discussions on the Internet is through Internet Relay Chat or IRC. The idea of IRC is that you use a special program (called an IRC client) to connect to one of the IRC servers located around the world. From here you can have things you type transmitted to computer users anywhere. All you need to do is join one of the discussion groups and off you go.
To help you along the way, here is some information about where to get the software and how to use IRC.
Where to Get the Software
How to Use IRC