I've not been in the game as long as some, or perhaps most of the members of this forum, but I will try to answer regardless.
Don't just think, do. By doing you learn to think like an engineer. You learn things along the way that will help you with other things you do, and by doing them you learn things that will help you with other...etc etc.
You are right about a course not being enough imo. As desireable as a certificate in this and that may be, it is rarely a true indication of someone's ability at electronics. Personally, I have studied EE to HNC level, started a degree but I am leaving it for a while, and in the mean time gaining some real experience.
In time you will learn what to look for in components, and datasheets wont be a mystery, you get a feel for it and things just 'click'. I can't say that this happens every time, but the more you do of your own projects, the more you learn and the better your ability will be overall.
Remember, finding a solution to an electronics problem often requires modular thinking, that is breaking the problem down into parts, and fitting them together. Take Dave's power supply project. You have the voltage regulation element, current limit element, microcontroller/DAC element, and while they feed back to each other, they can be seen as separate circuits. It's much easier to think that way than to try and analyse the whole thing at once.