* Learn to grok math. No, really. Learn to understand the physical meaning behind what you write. Time integral of some signal? Oh, yes! It's energy = ability of that thing to do work. Fourier series => this signal written as a sum of sine signals which you can analyze separately (with all the implications that has for linear systems). That kind of stuff.
* Learn to look at circuits in terms of transformation of magnitude, phase, frequency, shape and nature of signals, not in terms of connections, adapting this to various use cases in circuits. There's no general answer for this; an inductor is sometimes there to "insist on keeping the current to a constant value", sometimes it's there to exhibit a greater impedance to high-frequency signals, therefore allowing -- along with the capacitor over there -- only signals of a certain narrow frequency band to pass.
* Learn circuits in terms of idioms. Try to look at schematics and understand that "this part" is a filter, "that part" is a preamplifier, "that part" is a current mirror used for biasing and so on.
1) don't use a calculator. It's easy to plug numbers in without really understanding what they mean, and also believing a number that is several orders of magnitude out. And after the first week of converting between micro and nano and pico you'll have a good grasp on what those numbers mean.
2) draw circuits by hand. You'll be working on small circuits and drawing them is a bit like the "learn whTever the hardway" approach of typing stuff in.
3) for analogue DC circuits it's about manipulating current, voltage, resistance. For ac circuits it's power and impedance. For digital it's 1s and 0s and timing.
3a) in context components serve a role - decoupling or current limiting or amplifying or etc etc. you get to learn the configuration of a few components means an amplifier, and so you know that a voltage across those pins means a bigger voltage across those other pins.
Years ago the advice was to grab some second hand equipement and some new components and a breadboard and make circuits. The eauipment would be a powersupply, an oscilloscope, a signal generator, maybe a multimeter. The components would be a few resistors and capacitors and transistors with so e 555s and 741s. (With a few 4xxx series thrown in). Nowadays there is almost certainly a virtual set of this stuff that you can run on a computer. Perhaps some HN reader is involved in it?
The Art of Electronics (and the Student Lab book) used to be a solid introduction - hard work but good. I'm not sure if there's anything better for general use and I guess there's a lot of dated content. Microcontrollers is one example where you'd want additional books.
I'm like the OP's brother in that when I started EE, I had already been tinkering with circuits for about 7 years. Obviously, in labs it was a huge help, but it also gave the math and all the abstract concepts learned in class some relationship to the real world.
Having the background means you can glance at a circuit and immediately know that a certain resistor is sized too small, or hearing the high-pitched whine of an inductor means that may be the problem with your regulator. In short: build lots of different stuff, have it blow up in your face, and learn something from the experience.
