There are many different systems.
In your case, your polar express uses a transformer to supply power to the track. When you turn the power on, you then control the train through the remote control.
In other systems, the transformer itself has controls that adjusts the speed and direction of the train with a knob and other controls on the transformer itself.
Then there are other systems, DCC in this example, that supplies power to the track and sends computer signals through the track to a computer decoder in the train that controls speed, direction, sounds, etc.
I think this is beyond the scope of this thread. We've hi-jacked this thread and gotten way off on a tangent. I think you should look through the other forums on this site and there is a ton of information about all the different systems available.