Tom francis, developer of that great little indie game gunpoint, has been doing some tutorials using game maker studio. The free version as well i believe.
Great advice from everyone! I have some additional suggestions for learning resources:
When I was first learning how to program and make games, I found this book really helpful: http://www.amazon.com/Game-Programming-Teens-3rd-Edition/dp/1598635182 The title is “Game Programming for Teens” but I think the “Teens” part is a misnomer – what it really means is that anyone without programming experience should find it accessible.
That said, the language that book uses (BlitzMax) is not widely popular, so you might be better off with a resource like this one (it’s free too!): https://inventwithpython.com/ This online book teaches game programming in Python, which is a versatile language used by many programmers. Python is also easy to pick up for beginners: I know this because I taught Python at a programming camp for middle schoolers. Within a week I was able to teach them the basics of Python and even have them program their own games!
Also, a word of advice: be patient! It will take time before you can make anything bigger than simple arcade games like Pong or Asteroids. At least, that was my experience. 
Ta muchly. Been looking for a python learning resource.
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