Find out where a theme pulls its content from

Ok, I know my basic way around WordPress and I have dev tools that I use. I can make changes to things and make them work. However, I am at a loss with two templates I am playing with at the moment. The main problem is that I want to edit things to make them work better for my purposes. In this case that means making changes in the php. However, what is the easiest/quickest way to find out where the generated source comes from in a wordpress site? In these cases, I am looking for the script that generates the category overview of posts for the website and the script that builds the homepage. I thought I had found where to look, but then it turned out I didn’t. Extra hurdle is that it is a parent/child theme setup. What is the easiest way to track back where everything came from? I use firebug for css tracking, but are there other/similar tools I can use for php?