Wow, what are the chances!
I am currently completing the following specialization from Coursera - which my employer is paying for:
I would HIGHLY recommend it. You will learn about the various stages of software development, how to break down a project into small tasks / user stories, use this to build release plans, estimate time, and manage the client (as well as a LOT more).
Please note that I am not providing an affiliate link here. I am in no way affiliated with this program, but I do think it is quite good; it would answer 90% of your questions, and it has certainly made me a lot more comfortable with managing products/projects myself.
I personally AM a developer, but you do not need to be one to take this course, and you wouldn't suffer because of it.
If you don't want to pay the money, you could simply make a point form list of each lesson title and/or syllabus from each of the courses that comprise the specialization, and then go off and google-learn everything yourself.