I think you’re asking about free electron flow through a metal conductor which is way more complicated than you might like.
It’s worth learning about atomic orbitals, which are basically probability distributions around an atomic nucleus where electrons can be found in various conditions. There are many different patterns of these distributions, which represent different energy states possible for the atom, and their complexity increases in larger atoms. Here’s hydrogen:
Sometimes an electron transitions from a higher energy orbital to a lower one. Total energy is conserved, so the exact difference in energy levels between the orbitals is emitted as a photon of light. That photon has a very specific color (frequency) based on the difference in the energy levels of the transition. This is how neon signs work, with energy absorbed by the neon gas atoms and then very quickly emitted again as photons at the characteristic frequency.
That idea leads into quantum energy levels, spectral lines of various materials, spectroscopy, and beyond, even into astronomy with Doppler shifts of spectra indicating our relative velocity to a given star and the spectra themselves indicating the elemental composition of the star. But I’m getting off track.
A solid metal is mostly a 3 dimensional crystalline lattice of metal ions and a collection of delocalized electrons that can freely flow throughout the lattice. Another way to think of it is a lattice of atoms that collectively have an enormous shared valance electron orbital throughout which free electrons can move without transitioning energy states. That freedom to move is what makes them delocalized.
Note that each atom/ion only contributes one electron to the free pool. For example, Copper has 29 protons, which means it needs 29 electrons to be neutrally charged. In a copper metal lattice, each ion will still have 28 electrons bound up in its lower orbitals, and they won’t be participating in any electrical current flow through the metal.
This chemistry chapter attempts to explain that, and then goes on to give some very specific answers about the speed of electrons moving through your DC circuit.