As for what to study, I'd suggest looking more for building-block circuits than complete designs. Going over someone's schematic for a finished product will take forever, and you will probably miss major details. Instead, I'd get a good electronics text and study all the little circuits you find described in there. Analyzing them is not necessary--you only need to understand qualitatively what is happening (of course, sometimes you have to do the analysis to figure that out).
Once you know about a bunch of these "building blocks" (you really only have to know that they exist), then it's not so hard to choose a bunch of them to string together.