I want to be able to give out a form, with essentially 4 inputs. Each time it is submitted, I would it to trigger a python script.
I'm not totally sure where to start here. I could have the python code live on a server somewhere and have the google apps script trigger it, but ideally I could do this without having to host my code somewhere else. I also would like to avoid paying for anything...
Any and all advice would be appreciated. Please assume I have only a small amount of knowledge about this kind of stuff.
Check out this tutorial on the AppEngine documentation. https://developers.google.com/appengine/docs/python/gettingstartedpython27/introduction
It will help you set up using Python and WebApp2 (for your forms!) and storing this data to datastore if you wish. You could just expand and modify the guestbook tutorial they make you do to have your application/script do exactly what you need it to. It's an excellent tutorial to get started even if you don't have much knowledge about python or appengine.