Intro
You really can’t “figure it out all on your own.” That just isn’t possible, also there are about a zillion books on electronics and software and mechanics etc. So I’ll try to keep a list of my favorites here so that you can build a “Mechatronic” library of your own:
The Books
“The Art of Electronics” - 2nd Edition (or later) by Horowitz and Hill. This is truly the single best book you can own for electronics. It starts with a chapter on basic theory and moves briskly right to the good stuff. This will be a reference for you for the rest of your life so don’t skimp, get the student guide too. That way if you do the exercises to test your understanding, which I recommend, then you can check your answers.
“Power Electronics” - 2nd Edition (or later) by Mohan, Undeland, and Robbins. Published by Wiley. This is not necesarily an easy book to find but it has a great survey of the essentials of building circuits that have to control large currents. If you are building h-bridges or controlling things with your circuits, this book will help you get it done.
“Mobile Robots: Inspiration to Implementation” - Published by AK Peters, this book by Anita Flynn and Joe Jones (later if iRobot fame) was the go to book for all of the MIT 6.270 courses. It has very practical ideas for getting from “I want a robot that does …X” to building that feature.
“The Designers Guide to VHDL” - Written by Peter Ashenden this book is an excellent reference for VHDL. I consider it one of the essential texts for VHDL design work. Paired with Rajan’s book below it can really give you the knowledge you need to start programming FPGAs.
“Essential VHDL: RTL Synthesis Done Right” - Written by Sundar Rajan and distributed by XESS, is a really practical book about VHDL synthesis and design. It assumes you know VHDL syntax (Ashenden above is great for that) and goes on to give you an understanding of how that code synthesizes into practical circuits.