Python works on multiple platforms and can be used for desktop and web applications, thus I conclude that there is some way to compile it into an executable for Mac, Windows and Linux.
The problem being I have no idea where to start or how to write a GUI with it, can anybody shed some light on this and point me in the right direction please?
First you will need some GUI library with Python bindings and then (if you want) some program that will convert your python scripts into standalone executables.
Cross-platform GUI libraries with Python bindings (Windows, Linux, Mac)
Of course, there are many, but the most popular that I've seen in wild are:
Complete list is at http://wiki.python.org/moin/GuiProgramming
Single executable (all platforms)
Single executable (Windows)
Single executable (Linux)
Single executable (Mac)
Another system (not mentioned in the accepted answer yet) is PyInstaller, which worked for a PyQt project of mine when py2exe would not. I found it easier to use.
Pyinstaller is based on Gordon McMillan's Python Installer. Which is no longer available.