Note that the title above isn't "how to learn everything", but "how to learn about everything". The distinction I have in mind is between knowing the inside of a topic in deep detail — many facts and problem-solving skills — and knowing the structure and context of a topic: essential facts, what problems can be solved by the skilled, and how the topic fits with others.
This knowledge isn't superficial in a survey-course sense: It is about both deep structure and practical applications. Knowing about, in this sense, is crucial to understanding a new problem and what must be learned in more depth in order to solve it.
This topic was discussed intermittently on Overcoming Bias. Basic understanding of many fields allows to recognize how well-understood by science a problem is and to see its place in the structure of scientific knowledge; to develop better intuitive grasp on what's possible and what's not; and to adequately perceive the natural world.
The advice he gives for obtaining general knowledge feels right, even for studying the topics that you intend to eventually understand in depth:
Don't drop a subject because you know you'd fail a test — instead, read other half-understandable journals and textbooks to accumulate vocabulary, perspective, and context.