I'm in my second year of electrical and computer systems engineering at university.
What do you learn?
Mathematics: functions, matrices, series, differentiation, integration, differential equations, multivariable calculus, complex numbers, transforms, numerical methods, statistics.
Physics: mechanics, waves, quantum theory, electromagnetism.
Chemistry: matter, energy, material engineering, semiconductor principles.
Electrical Engineering: circuits, analogue systems, digital systems, signal processing, telecommunications, control.
Programming: C, C++, MATLAB, assemblers, compilers, operating systems, logic gates, CPU architecture.
What can you do with it?
Rather than state the jobs an engineering degree is used for, I think the most satisfying reward from my studies is understanding how things work. My understanding of computer science for example has helped me appreciate what happens when I turn a computer on, rather than just taking it for granted while I game or type on a word processor. Also, my ability to pick up on other people's bullshit is enhanced because I know the theory behind what they are saying probably better than they do. I love when people chirp about sound cards, for example, and have absolutely no idea about signal processing or electromagnetism to support their assertions.
How do you learn it?
I'm a reflective learner so I need time for ideas to make sense. My learning routine would be go to a lecture, write notes while I listen, go to the library and write more detailed notes on the lecture material, identify the concepts I don't understand, go to tutorials to ask questions, and do lots of exam-style questions. Working in groups really helps me too. You can talk with like-minded people to solve problems and collaborate together to increase your understanding and quality of work.
What do you think is the best way to learn?
Obviously the process of learning is different for each individual since we all have different genetics and we are all bought up in a very particular way. That said, I think for mathematics, science and engineering, the key to success is repetition and asking questions. The most successful peers I know solve as many questions as possible to gain insight and understanding, and the way they solve difficult problems is by asking questions.