One way to think of superposition is this: If particles behave to some degree like waves in the sense that they can never be completely "squeezed down" into actual points, then the waves -- the probability functions -- can add together very much like waves on a pond. So, just as on a pond surface you could combine together large waves with crests a foot apart traveling north with small waves whose crests are inch apart traveling east, you can in principle do exactly the same thing with the probability waves of an electron.
Wave addition is surprisingly simple, incidentally, amounting to not much more than simply imposing the smaller wave onto the moving surface of the larger wave. So, while the heights of the waves at any one point will change as the two waves move, the height of the wave at that point will always be nothing more than a simple arithmetic sum of the heights that each wave would have had separately. That nice, simple arithmetic property is called linearity, and (fortunately for physicists seeking simplicity!) it can be found throughout much of physics.
In the case of the electron there is one additional constraint: A single electron can only generate a finite amount of wave action. That wave action can be split up in many different ways and into many different types of waves, but the total sum of all those waves must always add up to one "electron's worth" of wave action. So for example, just as with the pond waves, an electron wave could consist of an equal mix of large waves moving north and small waves moving south, as long as the two sets of waves always add up to "one electron" of total wave action.
Now the fun part is that when electrons are modeled as waves, those waves have a very specific meaning, one that is a bit less than intuitive. The interpretation is this: The big waves traveling north mean that if you poke hard at the wave with something like a photon, you will sometimes (half the time if the two wave types are equal in strength) find an electron moving north, rather slowly. However, the instant you find the electron by using such a poke, all of that wave interpretation "instantly" disappears. (I say "instantly" in quotes because that is a very loaded term in that context; but that's for some other answer!)
However, since there are two types of electron waves added together, that same poke is just as likely to find the electron moving east at a much faster clip, which is what the more tightly spaced eastbound wave means. Once again, if a poke finds the electron moving east, all of the wave interpretations cease to have meaning and you simply have an electron that look a lot more like a particle in terms of where it is located.
Once found, the electron becomes a candidate for creating new waves and starting the process all over again. That is what happens with conduction electrons in metals, for example. Or, alternatively, it could get captured by a heavier object such as an atom, and at that point it would cease to behave like a roaming wave.
However, even then the electron does not stop behaving like a wave. In fact, the entire discipline of chemistry amounts to a detailed mapping out of what happens when the many different waves possible for a charged electron become bound into a tight, cramped, and mostly spherical space, one in which it must argue and negotiate and continually bump into other electrons in an attempt to find its own little bit of turf. From these waves and the intransigence of electrons (called fermion behavior) to pack together tightly comes all of the rich behavior that makes matter and life possible.