How does it work? Here’s how Piper Nillson explains it in her Design and Composition class.

“The proportions of the golden section are 1:1.618.

“A golden rectangle follows a stricter format. It is built with the same ratio as the golden section, 1:1.618. However, the left segment is a perfect square.

A golden rectangle can be drawn from a square. First, draw a diagonal from the corner to the midpoint. Then extend it into an arch.”

 
Voila! You can see below that the proportions of the golden rectangle are 1:1.618.
 

The following is not quoted from the course, but my own content that I felt would be useful here, as a step by step creation of a Golden Rectangle:

You can also use simple math to apply the Golden Rectangle.

Suppose you want to create a golden rectangle in your composition.

Begin by deciding if you want a landscape (wider than tall as shown above) or portrait design (taller than wide).  I’m going to make a landscape design.

First, figure out how tall it will be. I’ll use 64cm.

Then multiply 64cm by 1.62 (the Golden Ratio) to get your width, which is 104cm.

So the dimensions of your Golden Section are 104cm x 64cm.