The final step in making the scripts run when double-clicked (which also means they can run outside of the ArcGIS environment, saving lots of memory overhead) is to associate files with the .py extension with the Python interpreter. If the scripts have not already been associated with the interpreter, they will appear as files of an unknown type or as a text file.

To change this, right-click on a Python script. Select Open With, and then select Choose Default Program. If python.exe or pythonw.exe does not appear as a choice, navigate to the folder that holds them (C:\Python27\ArcGIS10.2, in this case) and select either python.exe or pythonw.exe. Again, the difference between the two is the appearance of a terminal window when the scripts are run using python.exe, which will contain any output from the script (but this window will disappear when the script is done). I recommend using pythonw.exe when executing scripts, and python.exe to test...