You can just drag a file onto your desktop from your file manager to copy it (or link it) to the desktop. That should create an icon for the file on your desktop in most Linux distros.
To allow the system to run your script you need to ensure that the script starts with a proper shebang line, eg
#!/usr/bin/env python
and that the file has execute permissions. Your file manager will have some menu command to modify file permissions. Or you can just do it in the shell with
chmod a+x application.py
.
If you've created a link to your script on the desktop you'll need to modify the permissions of the original file, not the link, since links don't have permissions themselves.
Then you can single-click the icon to launch it.