I'll just look at the interesting case of a plate with charge $Q$ facing a neutral plate.
In the plate dimension >> plate separation, uniform field approximation, the charges on the plate surfaces are:
$+Q/2$ on each surface of the charged plate. $±Q/2$ on the surfaces of the neutral plate, with $-Q/2$ on the inner (facing) surface and $+Q/2$ on the outer surface.
Taking account of the charges on all 4 surfaces, and the fields that they give rise to, you'll find that the resultant field inside each plate is zero.
How does this surface charge distribution come about (given the overall charges of $+Q$ and 0 on the plates)? By movement of free electrons within the metal of the plates. If there is a net electric field within the metal the free electrons will move in the direction of the field, though frequently colliding with the lattice. Suppose that the neutral plate was put in position near the positive plate and had, at one instant, charges of $±Q/4$ on its surfaces. There would then be, it is easy to see, a resultant electric field inside the neutral plate so the free electrons would be moving. Movement would stop when the charges on its surfaces were $±Q/2$, as the electric field inside it would be zero.