Firstly, the technique you describe is actually called "Moving together" at least by British climbers. The technique is used to move rapidly on relatively easy ground while also providing a degree of protection from falls. It is also used to rope up while crossing glaciers.
This website has a good set of photos showing how to attach the rope to your harness and coil it around the body. The knot is a simple overhand knot which is tied around the coils and clipped to a carabiner clipped to the loop formed at the rope's attachment poin to the harness.
As to the distance to keep between climbers, that depends on the terrain. This page on the British Mountaineering Council's website gives a description of what sort of distances to keep between roped climbers while moving together.
You can change this distance by "taking in coils" either for a long period by untying the knot and letting out coils or adding coils around the body or if only for a short distance, maybe on easier ground between more tricky parts, by simply taking in a few coils and holding onto them in your hand (usually the climber in the rear would do this).
While moving together on say a rock ridge, the climber in front can place the rope alternately behind any spikes or flakes and the other climber than removes the rope from the spikes or flakes. You could also place the odd piece of artificial protection in the same way. As the ground should be relatively easy, the distance between these running belays need not be close together.
The reason for this technique is that it is much quicker than "pitching" a climb in the normal way but still provides some protection on the event of a fall.