The speed of electricity through a wire is a bit of a complex question. It
depends on whether you are considering the rate at which electrons
themselves flow along a wire or whether you are considering the rate at
which an electrical signal passes along a wire.
In the first case, electrons themselves move quite slowly - about 100
micrometres per second (or, from another perspective, 1 metre in about 2.8
hours!) Clearly, this is not what we observe when we turn on a light switch.
Ideally, electricity moves at the speed of light. Imagine a tube full of
marbles. If you push a marble in at one end of the tube, another marble pops
out the other end almost instantaneously. Even if the individual marbles are
moving very slowly, the marble "wavefront" is travelling at a very high
velocity.
In the real world, things are not quite so tidy. Electricity flowing through
a gas, or having to work its way through electronic components such as
resistors or capacitors, can be slowed to speeds of 60 to 80 percent of
light speed. However, that's still fast enough that you can safely expect
the light to come on as soon as you flick the switch.