How can a total, complete beginner read source code?
To understand source code in any language, you first need to learn the language. It's as simple as that!
Usually, reading source code (as a sole activity) will hurt your head without giving much benefit in terms of learning the underlying language. You need a structured tour through carefully chosen small source code examples, such as a book or tutorial will give you.
Check Amazon out for books and Google for tutorials, try a few. The links offered by some of the other answers would also be a great starting point.
I am a complete, total beginner in programming, although I do have knowledge of CSS and HTML.
I would like to learn Python. I downloaded lots of source code but the amount of files and the complexity really confuses me. I don't know where to begin. Is there a particular order I should look for?
Thanks.
EDIT: Sorry guys, I forgot to mention that I already have both the online tutorial and a couple of books handy. I basically I don't quite understand how to "dismantle" and understand complex source code, in order to grasp programming techniques and concepts. 
EDIT2: Thanks for the extremely quick comments, guys. I really appreciate it. This website is awesome.