Atoms contain several layers or shells of electrons. The hydrogen atom has one electron on the first layer, the helium atom has two on the first layer, the next atom (lithium) has two on the first layer then one on the second layer, etc. Each layer can typically only hold a specific number of electrons.
The best conductors have one atom in their outermost layer, and they are more than happy to give it up. Consider the atom of copper. It has the following electron count in each layer: 2, 8, 18, 1. It will give up that one electron under a weakly charged field, and it will then be positively charged and "pull" an electron from a neighbor copper atom. If you look at silver and gold they are arranged in a similar manner: 2, 8, 18, 18, 1 for silver, and 2, 8, 18, 32, 18, 1 for gold.
You can strip any atom of an electron, but the best "conductors" require only a weak field to do so.
So if I pull an electron off the end of a copper wire, using a weak electrical field, then that atom might pull an electron off its neighbor, and eventually one copper atom somewhere in the wire will lose their electron, but be unable to get someone else's because they're too far away, or interacting with some other field. If I push an electron in the end of the wire, then the copper atom that gets it will have too many, exhibit a negative charge, and essentially push its extra electron onto some other copper atom until it finds an atom that can't get rid of it, or an atom that's missing one already.
You can push and pull electrons onto and off of insulators as well - you do so when you build up static charges, for instance, using cloth and plastic.
But conductors redistribute the charge internally, so if you charge one end of a wire with extra electrons, you can consider the other end of the wire similarly charged.
A battery, often using a chemical reaction, sets up a positive charge on one end, and a negative charge on the other. If you connect a conductor between the two ends, you will force electrons through the conductor as they travel from the negatively charged side (too many electrons) to the positively charged side (too few electrons).
The electrons move one direction only for DC, and they move in one direction then the other for AC. Due to the changing magnetic field (ie, the wire becomes an inductor) high frequency AC signals typically travel near the surface of the wire. You can look up "skin effect" to understand this better. The electrons travel between the atoms of the conductor.
Every time you push 6.28x10^18 electrons through the wire, you've moved one amp of current. That's 6.28 billion billion electrons. However, there are about 4.38x10^22 copper atoms in one meter of 20gauge wire, so if you push a full amp through it, assuming even distribution, you won't get any of the electrons out that you pushed in - you'd have pushed out electrons that were already in the wire. Electrons move slowly, individually, but the charge distributes quickly - as soon as you push in one electron, you find that it's easier to pull one off the other end almost at the speed of light at the other end. It's not the same electron, but the effect and charge is the same.
A good conductor distributes the charge very, very quickly, and doesn't convert much of the movement to heat. If you push the same current through the same size gold wire and the same size copper wire, the gold wire will heat up more, because it's harder for those gold atoms to give up and accept electrons.
Best Answer
Do electrons migrate from the source to the dielectric? No. They flow from one plate to the other plate.
Imagine a capacitor disconnected from everything, with no energy stored in it initially. This means that each of the two electrodes has a net charge of 0. For example, if each electrode/plate has million protons, then it must also have a million electrons.
Now let’s connect a battery to the cap. What happens now is that the battery pumps a percentage of the million electronics from plate1 (connected to the plus side of the battery) to plate2 of the capacitor. This flow of charge (current) goes through the battery (since the 2 plates are electrically isolated by a dielectric), and into the other plate, until the cap reaches the battery voltage. In this sense, the electrons migrate from the source to the plate.
(Imagine the battery as a water pump, and the water molecules are the electrons particles. Yes, you can imagine these as "little rolling balls that leave the battery".)
Now once you disconnect the battery, the electrons that have already been pumped onto plate2 remain there since the two plates are electrically isolated.