A complete computers and electronics curriculum
The fields of computers and electronics, though separate, are inseparably linked. You can't really understand one without understanding the other. While many colleges and universities offer majors in both fields, few provide majors that combine the two, and those which do typically do so by simply mixing together a hodgepodge of classes from either field which fails to actually provide a link between these two important worlds.
This, along with lack of time/money to pay for a(nother) college education, leads many people to self-study. So, here's a basically complete list of things you should learn if you want to truly understand computers and electronics, starting with the absolute most basic concepts and proceeding from there. The mixture of these subjects isn't perfect, but I've deliberately tried to implement hard breaks from certain subject matter so that you can let some of what you've learned seep into certain parts of your brain while you go off to learn some distant, relatively unrelated subject. This organization is fairly non-random, but there is a bit of randomness to it to keep things fresh and exciting.
Almost no post-high-school knowledge is assumed. You should know how to do basic arithmetic and algebra, but no understanding of calculus or special physics is needed to start.
The first thing you should probably learn about is the atomic structure of matter. Learn about the fundamental particles--protons, neutrons, and electrons--and how they fit together. You should know that protons have a positive charge, neutrons have no charge, and electrons have a negative charge.
From there, learn about elements. You should also keep some specific elements in mind, which have particular importance in the fields of computers and electronics, notably (in alphabetical order):
Arsenic (for its use in semiconductors)
Carbon (for its use in resistors)
Copper (for its use as a conductor in most wire)
Gallium (for its use in semiconductors)
Germanium (for its use in semiconductors)
Lead (for its use in solder)
Silicon (for its use in semiconductors)
Silver (for its use as a high-efficiency conductor)
Tin (for its use in solder)
Now you're set to learn about conductors and insulators. Learn why copper is considered a conductor, while air and rubber are insulators. Also briefly recognize that a semiconductor is something that sort of conducts but not very well; you'll learn much more about semiconductors later.
At this point, you're all primed to learn the three fundamental quantities of an electric circuit: Voltage, current, and resistance. Learn what each of these is, and when you've done that, you're ready to learn Ohm's Law, one of the most important laws in electronics. It's quite simple to understand once you get it, but it's useful in almost everything.
Up until now, I've only been talking about electronics. However, as you do this, you should also be learning about computers. This curriculum assumes no special knowledge of computers, but you should be at least generally computer-literate in the sense of being able to use a computer (although if you weren't, you probably wouldn't be reading this on a website right now). In any case, if you're not up on computers, now might be a good time to start using them, learning about the basics of how to use different applications and operating systems. If you're already computer-literate but have never done any programming, you might want to start experimenting with the basics of some programming language, like perhaps BASIC.
Getting back to electronics, you should learn about DC (direct current), and what makes it different from AC (alternating current). Note that although many people use the term "AC" to specifically mean a repeating waveform like a sine wave (especially the sine wave formed by electrical power as it exists in the wall socket of a typical house), "AC" can also mean any non-repeating electrical or electronic signal, such as an audio wave.
Next, you'll want to learn Kirchhoff's laws. There are two: Kirchhoff's Current Law (KCL), and Kirchhoff's Voltage Law (KVL). Both of these are most often applied to DC, although they could be useful for AC as well.
Now it's time to do devices. There are several fundamental devices in electronics, and at some point or another, you might as well just go through the basic ones so you know the fundamental building blocks of a circuit. Besides the absolute most fundamental parts like a power source (such as a battery) to supply voltage, and wires to carry current, devices you'll need to learn about for starters include resistors, inductors, capacitors, and transformers.