Like a lot of folks, as a teenager I thought of electricity like “water in a pipe”. But I think this analogy is fundamentally unhelpful because when you apply pressure (“voltage”) at one end of the pipe it is easiest to think of it as instantaneously appearing at the other end of the pipe (assuming the pipe is full of water). Perhaps if I had thought of it as “empty pipes” that would have been a better mental model.
That's also how I learned the basics in 4H club. I also think it's a bad analogy. Water runs downhill. The explanations and illustrative diagrams always confused me because I couldn't figure out how gravity fit into the picture. Nowadays I think of it as *air pressure.* This is not necessarily better, I guess, but at least it makes sense to me!
One thing that might help, maybe, is to notice that there is not really any such thing as a "signal" moving in the wires. The idea of "signal" is an abstraction that lets us think about logic instead of electrons. Similarly, "voltage" is not a thing that moves around. Voltage is a measurement taken by us, the observers, that describes the relationship between two points in a circuit. What we are measuring, specifically, is the number of free electrons (or "electron holes" that free electrons could move into). In the classical model, because Ben Franklin was a bit of a goober, the point that has more "electron holes" is positively charged, while the point that has more free electrons is negatively charged. If you connect the two points with a conductor, the free electrons will move from the negative point to fill in the holes at the positive point. Classical current is the movement of the "electron holes" in a conductor, but what is really happening is that electrons are zipping around in the *opposite direction.*
Ideally, all points in a circuit that are electrically common have the same voltage (0V) when compared to each other. If we add some "electron holes" (say by attaching the positive terminal of a battery), we can "see" them at all the points electrically common with the battery. (I mean, if points A, B, and C are electrically common and we attach a 9V battery to point A, when we measure voltage between A and B or A and C we don't see 9V; we still see 0V.) This is (at least for CMOS logic) what enables the digital signal abstraction.
Suppose we want to send a signal from (say) a clock generator to (say) a 6502 processor. We make the 6502's clock input pin electrically common with the clock generator's output pin (we connect them with a wire). To send the signal, the clock generator changes the voltage on its output pin. That changes the voltage at the 6502's clock input pin. All the 6502 has to do is "notice" that the voltage has changed.
Ideally, all points in a circuit that are electrically common have the same voltage (0V) when compared to each other. In reality, though, electrons move very quickly, but *not instantaneously.* So, it takes the tiniest bit of time for the battery to "suck" the electrons out of the circuit and charge up points B and C. How long this is depends on how big the wire is, what it's made of, and what else is going on around it. But more importantly, to change the voltage at the 6502's clock input pin some electrons must move. Those electrons come from somewhere! Where? The answer is ground. The ground side of a circuit is like a free electron reservoir. If some electrons go out from the clock input of the 6502 into the clock output of the oscillator, then the same amount of electrons must also go into the 6502 through its ground pin. This means that, temporarily, the 6502's local ground pin is slightly more positive than the rest of the ground side of the circuit. Meanwhile, the oscillator has a few extra free electrons that it just received from the 6502. It has to send those electrons back to the 6502 so that the free electron reservoir can settle down. If you don't suck, you can't blow.

This is the signal return path. Unfortunately (in some ways) for us, electrons like to take the path of least resistance. If the loop back between the ground pins of the oscillator and 6502 is long or windy those electrons will try to find some other way to go, which can include through other ICs that might happen to be in the way. Havoc may ensue.
Moreover, as the oscillator switches voltage at its output pin and the 6502 follows almost (but not quite) instantaneously at its input pin, tiny amounts of current will be constantly flowing back and forth between those two pins, and also between the two ground pins of those ICs. Even though our (logic) signal is (abstractly) traveling in one direction (from oscillator to 6502), we are actually dealing with alternating current! We potentially have to think about capacitance, inductance, impedance and all kinds of complicated math. Because of electromagnetic fields we might experience intermittent glitches on a signal caused by complex relationships between switching patterns of *other signals.* This is why Ed keeps talking about rules of thumb. To debug these sorts of problems you need (often very expensive) equipment, and a real command of electronics math. This is something that most hobbyists (including me!) would rather avoid.
Finally, I guess it's worth pointing out that even the classical model is not "what's really going on." As Ed says, you can go all the way down to quantum mechanics, where electrons are not "things" that "move" but are more like ripples in fields. Every model is a description in some sort of language, more or less precise, of what we observe. There is no "what's really going on" that we can access independently from our perceptions. At some point you have to stop looking for the next turtle down and start building computers.
