How should I go about independently studying physics and quantum mechanics?
I don’t have any money for college, but could probably afford a text book and study various online science journals. I’m just extremely curious and interested in those ideas and would really like to expand my horizons, despite my lack of time and money for college. BTW I did very well in physics and math in high school.
Just go to the library and take out books on the subjects.
Books by Michio Kaku are great.
Brian Greene’s "the elegant universe" is really good.
Also Kip Thorne has great stuff on black holes that will blow your mind.
What is it exactly that you want to know about QM? See, QM is nothing that you will encounter in your everyday life, nor will it get you a job. Classical physics is a lot more useful and it is something you can literally do experiments at home; there is no way you can do a QM mechanical experiment without serious equipment.
Many people claim they "understand" QM simply because they read a few books on popular science. They have no idea what QM really is and it takes literally years of training in advanced physics and advanced math to really get a grasp of it. You can read about it if you want, but it really won’t amount to much.
If you really want to learn QM on your own, you need learn standard mechanics, electrodynamics, thermodynamics, multi-variable calculus, differential equations, partial differential equations, complex variable analysis, linear algebra, probability, statistics, and a course on modern physics. That is before you even start learning about QM! Good luck with that.
The answers above offer good advice. A helpful website is http://www.physicsforums.com/. They mostly discuss new research being published, but they will regularly answer questions related to homework or curiosity.