arcgis 10.2 - Debugging ImportError: No module named arcpy?

I have written a script and am trying to run it in Python IDLE 2.7.6.

I first try to import arcpy, but I get an error message saying:

ImportError: No module named arcpy

Why does it not work?

I am using ArcGIS Desktop 10.2.

Answer

This error is discussed near the bottom of the Importing ArcPy documentation page where there are some additional notes about ArcGIS 10.2.1 (if that is the precise version that you are using).