Knowing exactly what each component does, and what effect it has when combined with other components is paramount to understanding more complex circuitry. Even in a digital system there is a chuck of analogue stuff which will really confuse you if you don't know what it does (and whether it affects the operation of the digital part).
Apart from the basics, the rest is all exposure really. Finding out how some effect is created, what techniques they've used, why they work the way they do, you'll learn all of this as you are exposed to more and more circuitry. You will definitely get overwhelmed if you try and learn everything though. For basic exposure an undergrad introduction textbook will serve you fine, once through that find out what your really interested in and read the recommended textbooks from any university.
Just fyi, in my electrical degree there are about 5 streams which you can specialise in, each which take about 2 years of concentrated study. And that's just at undergraduate level! (I'm in australia and our university system is different to that of the US, an undergrad ee degree is 4 years straight out of high school)