I want to be able to call functions that I am writing in a Chrome extension from the JS console in Chrome, so that I can test them easily and see how their output changes as the page changes.
But it seems as the functions I write aren't available to the chrome JS console. I don't really understand JS that well, or the chrome extension model, but I need to somehow inject the extension source into the body of the page that I am using the extension for?
If you are talking about functions that you defined in a background page, then you need to go to your extensions page, check the developer mode box, and click on _generated_background_page.html. That is where you will find your background page code.
If you mean functions in a content script, then when you are in the console, go down to where it says <page context> and change it to your extension. Then you will have access to the functions in the content script.