There are some situations when you need to start a second X session on your computer.

If you are running KDE the solution is quite simple, just go to

K->Leave->Switch User

and if you are not using KDE, the solution is still easy :),

Hit ALT+CTRL+F2

and log in the new terminal window, now run inside it.

xinit -- :1

A new X session will start, now you can switch between them using

ALT+CTRL+F7, F8

You can also start a third one, using the third terminal, and so on.

Another way is to run

startx -- :1

Instead of xinit, be sure to use :2 or :3 when :1 was already used, to start multiple X sessions.