I started at around the age of five with a screwdriver and a wall socket. Once I had built up an immunity to mains shocks, I moved on to old TVs. By the time I was 12 I could (a) fix most old TVs, and (b) take 20kv through the fingers without flinching

Actually, I can't really remember when I started seriously working with this sort of thing. I certainly made pocket-money from 11 or 12 onwards by recovering old electronics from the town dump, repairing them, and selling them on to friends. I read a lot of books on the subject of electronics, but during my school years there was no formal education in it. I actually trained to be a chemical engineer, but ended up in electronics and mechanical engineering by default. Runs in the blood, I guess, based on several past generations on both sides.

For someone starting out now, I can recommend the Art of Electronics book mentioned in another reply, with the caveat that it's pretty heavy in math. If, like me, you have some difficulty with abstract maths, it can be heavy going in some chapters. That said, it's the definitive reference in the field, and full of very good information, starting from the basics and going up to some fairly advanced if slightly out of date stuff.

I could also suggest finding some of the better electronics hobby magazine with diy project in. These are, at least in the UK, harder and harder to find, but the majority of them seem to still be going although usually only via subscription. Titles such as Electronics Today International, Practical Electronics, and the best one of the lot Elektor. They have loads of constructional projects from simple to very complex going back decades in the archives, and an awful lot of good practical information.

One of the problems nowadays compared to when I began in the late 60s, early 70s is that the costs and entry requirements to home electronics design have risen substantially. This is almost entirely down to the advent of surface-mount techniques and vastly higher integration of modern parts. When I started, you could do most things with a reasonably soldering iron, a bench power supply, a good multimeter and lots of patience. Parts were available from numerous shops, and everything was of a size that made it easy to work with.

Now, of course, it's difficult to design and build anything beyond the most basic stuff without a fairly large amount of equipment. Parts are more difficult to source, usually only available via mail-order from specialist suppliers, and most of the more interesting things are surface mount. This isn't really a major problem, but does require more investment and skill to work with. The majority of the electronics hobby shops have either vanished or become consumer electronics outlets.

It's certainly not impossible to just pick things up by yourself now, but it is considerably more difficult than it used to be. A beginner can't, for example, take most old consumer devices and take them apart for practice, as the amount of experience, skill, and equipment required is significant.

I mean, looking around my workshop at the moment, I have three oscilloscopes, two of them digital storage ones, a logic analyser, a spectrum analyser, a very good temperature controlled soldering station, a frequency counter, at least three multimeters, several drawers full of specialist tools, and the gods alone know how many components and other detritus. Not to mention three computers, a pic programmer, a universal device programmer/emulator, lots of expensive specialist software, and so on. At a conservative estimate it's about 20kiloquid worth of kit, and probably at least as much in parts. A lot of it was actually second hand or samples, but you get the idea. It takes time and effort to acquire the equipment, and without it you're limited to pretty simple projects. Not to say that those can't be very rewarding and teach you a lot.

While this may have drifted a little from what I set out to say, hopefully you can get some useful info from my ramblings

pca
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Experience is what you get just after it would have helped...