How fast do the electrons travel in copper? Not as fast as you might think. A tortoise is much quicker.
The drift velocity at a safe current density (say 1A/mm2) is ~0.08mm/s, so slow you might wonder how a wall switch is able to turn the ceiling light on, never mind a how multigigabit/s serial link works! It takes over ten hours for the electrons to get from the switch to a light bulb 3 meters away.
Of course, the drift velocity is just the average velocity. The free electrons in copper are colliding back and forth at the Fermi speed of 1.57×106m/s. (Fermi speed is a whole other topic.) But this speed doesn’t “move the ball forward” because random collisions mean an electron is moving away from our light bulb almost as often as toward it. One mean free path forward and nearly one mean free path backward (or sideways). And the Fermi speed is still much lower than the speed of light that we all know is the right answer.
What’s going on?
Well, to get energy or a signal from the source to the load it isn’t necessary to move a specific electron from the source to the load. Think of the domino effect, or a ripple on a pond. The individual dominoes and water molecules need not move all the way for the wave to propagate energy. They just have to shove their neighbor a bit. In our copper traces, the shoving is done by the EM wave which does propagate at the speed of light in the dielectric around the wire.
The drift velocity is (vd = J/(qn)) where J is current density, q is the elementary charge ~1.6×10-19 C, and n is free electron density (~8.47×1028 electrons/m3 for copper).