No, the user does not walk around while using VR. That would be extremely dangerous as your are effectively blind to your real-world surroundings. You could stub your toe on your coffee table, or fall off a cliff, depending where you are.
VR relies on some sort of stationary controller. Whether it be keyboard and mouse, PlayStation controller, or Kinect sensors reading body movements, in all cases the user generally doesn't move more than a foot or so from their location while wearing the vision-impairing head unit.
Augmented reality, on the other hand, does allow the user to move around and interact with the real world in some enhanced (i.e. augmented) way. An example of an augmented reality device would be Google Glass.