For me, it has never been fully satisfying simply to build a circuit that someone else has designed. My personal pursuit has been to learn how to design circuits for myself that will obey my own whims and desires. This allows me to select my own components and decide my own trade-offs and parameters. Finally, I find it very satisfying to design something and see that work as designed.
The ability to engineer circuits seems like a daunting task at first. Yet I find that if you keep chipping away at small portions of the science, you can succeed over time. As a hobbyist, I am still in pursuit of the necessary skills and science. I have dedicated this area to sharing information that I have learned along the way that might be helpful.
This page is dedicated to analog electronics. I feel that digital electronics is best covered somewhere else and is a huge topic onto itself.
One thing that has helped me a great deal is acquiring the right text books. In my opinion, there is no one “right book” for everything. This is a list of books that I have found to be helpful:
Some of these books are very expensive new. I highly recommend that hobbyists acquire these books used when possible. The most difficult one to acquire at a good price is “The Art of Electronics” book. This has been a hugely successful book and may be out in the 3rd edition by the time you read this (end of 2011/2012?). But I consider this a “must have” book if you are interested in analog electronics. I wouldn't worry too much about getting the latest edition. The sections on analog topics will still be applicable today. Clearly the digital chapters are dated, but there are better books if you're interesting in that.
The “Microelectronic Circuits” is also a “must have” in my opinion. It is considerably more detailed in many places than the former. This book will help you understand how the mathematics is derived for the components being studied.
It is suggested that you have a basic grasp of electronics to get the most out of these articles. You should have a good understanding of: