I'm not a PhD student or anything, and don't intend to go to school for astronomy or physics. I'm an author who's always enjoyed space, and I want to use amateur astronomy as a way to contribute to the field. Send my findings to a team and the like. It's a fun hobby and I'd like to be helpful, even if I have no intentions of being a professional in this field.
However, despite my interest in space, I have zero research experience in astronomy. I made an A in conceptual physics in college, and my highest math is precalculus. I tried trigonometry and calculus, and I was defeated. I'm not adverse to using trig and precalculus, though, and I have an entire internet to make sure I get the math right. I'm going for correct results with a casual timeframe, not a C average with tests on the horizon.
Aside from reading white papers on Arxiv and textbooks I buy secondhand on ebay, or contacting professionals directly for information on what's currently being studied, I'm not really sure where to begin. I don't have a (working) telescope, and there looks to be a lot of different subjects I can study. Where do I begin with the basics? What are ways I can quickly and actively apply what I read? Thanks for any information you can provide in advance.
You can participate in citizen science projects, requiring no special knowledge or equipment, such as those hosted on Zooniverse.
With a fairly serious amateur telescope, you could potentially discover new comets, asteroids, or other minor solar system bodies. Or you could pursue astrophotography.
But there's no realistic way of directly contributing to published academic research without professional training and experience.