Electrons are pretty much free to move about anywhere in and on a conductor. They will bump into things, scatter and give off energy, which is how resistance arises, but as long as you provide a force on the electrons you can move them anywhere in the conductor. An electric field, to which the electrons are directly responding to, induces a force on the electrons. However, when an electron moves from its desired place in the conductor's lattice, it leaves behind a region of slightly positive charge since it must be taken from a neutral atom. So now we have a local area of net positive charge where the electron was taken from and a local area of net negative charge where the electron is taken to. This creates its own electric field, one that opposes the applied electric field that moved the electron in the first place. So as we start displacing electrons with an applied field, they create a charge difference that creates a canceling electric field too.
So we end up moving the electrons to the surface of the conductor because that is the only real obstacle to their movement. The idea is, as long as there is a net field inside the conductor, the electrons will experience a force and will move to create a field to cancel out the applied field. So they naturally arrange themselves so that there is no net field inside the conductor and to do this they build up on the surface of the conductor.
That is what happens in the static case. In the AC case, a signal is propagated down the wire by electromagnetic waves. These waves are traveling electric and magnetic fields. The changing electric and magnetic fields will induce forces on the electrons just like they did before in the static case. And just like before in the static case, the resulting movement of the electrons will create fields that cancel out the applied fields. The result is that currents are induced in the conductor that create secondary waves that cancel out the incident waves. A conductor has very little resistance (zero if it is perfect) which means that the electrons can move almost completely free. Thus, they can respond almost perfectly to the incident fields. Since they can respond almost perfectly, the surface currents can completely cancel out the incident fields. So the fields are canceled out before they have a chance to penetrate into the conductor to induce movement of electrons inside. So that is a brief conceptual idea of why AC currents also only flow on the skin of a good or perfect electrical conductor.
