Cyanmonkey,
Having no formal electronics training I'm find myself in the same boat.
I always feel like I'm not part of club whenever I don't understand what's going on. And those who do understand are rightfully proud of their knowledge.
Typically I consider that there are 3 things to know:
1. Theory - The general why/how stuff works.
For this I suggest this book for < $20:
http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?z=y&isbn=0760752397&itm=1
2. Detailed Design - eg. Using a spec sheet, how do I know which resistance will provide 35 dB gain using a XXX opamp?
To answer this I would first formulate the right question and then get someone on this board to show some example calcs. Although to truely understand what's going on, I think you'll need to build test circuits and prove to yourself that the math works. Having the equations in front of you isn't enough.
3. General Design - eg. I want to build an opamp of my own design from scratch.
Of course this is hardest thing to grasp since it requires years of experience. I think we'd all like to be the next Rupert Neve, but the fact of the matter is that a successful circuit will always mimic something that alread exist. Improvement in general design comes to us after years of building and pondering over countless pages of schematics.
The idea is quite simple: Copy and modify. After some time you'll end up with something unique.
This is my $0.02. Should you find the route to instant knowledge, please do share it on this board.
Regards,
- Andre