When you flick a light switch the light comes on straightaway. A common misconception is that this is because the electrons leave the power supply and travel very quickly through empty wires and then back to the power supply again.
In fact the electrons are already there everywhere in the circuit and they all start moving very slowly at almost exactly the same time. Just like a wheel, there's no part that begins first.
If you look a little more deeply there are actually three very different speeds, which are very difficult to imagine all at the same time.
1. (VERY FAST) The random thermal jiggling of the electrons. The electrons whizz around colliding billions of times a second with the surrounding atoms (or, more accurately, ions). This depends on the metal and the temperature but is typically around 1% of the speed of light.
2. (VERY VERY FAST) The speed at which the electrons find out that they should start moving. Think of the rear carriage of a train starting to move at almost exactly the same time that the locomotive begins to pull. This is called the signal speed and is typically a bit less than the speed of light.
3. (VERY VERY SLOW) The speed that the electrons actually make progress along the wire. This is called the drift speed and is typically around half a metre an hour - slower than a snail. This is because the electric field in the wire (think push from the battery) doesn't have much space to accelerate the electrons before their high thermal speed causes them to be scattered off another atom.
In this simulation I try to show all three speeds at the same time.