Mechanical tachometers work exactly the same way as a speedometer does. There is a cable that runs from the camshaft or distributor to the gauge.
The old electric analog tachometers work the same way, but replace the cable with an electrical circuit. The way it works, in mathematical terms, is that first the waveform from the distributor is normalized for amplitude, then fed to a trigger circuit which creates pulses of a pre-defined width to normalize out the dwell factor of the distributor. Then that signal is fed into an integrator (same as a low-pass filter), which measures the power of the signal. Then the integrator feeds the analog meter movement, which deflects the needle linearly with applied power. Since power is proportional to RPM (frequency) with a constant amplitude, it all works. The tachometer is calibrated by either adjusting the R-C time constant of the integrator or the width of the pulses. An integrator is a circuit that performs the calculus function of integration by charging a capacitor (C) through a resistor (R).
Other tachs use the method given by Oly's site, which is really the same thing but it uses the meter movement itself as the integrator rather than a separate circuit.
The separate electrical integrator makes the meter movement design less critical and keeps it from being overly twitchy. It also allows a switch for switching between 4-6-8 cylinder configurations and allows use on engines with uneven firing orders (like Buick oddfire V6's)
The newer tachometers are actually digital and use a frequency counter circuit. The clock is provided by a crystal oscillator just like in a watch. The meter movement is driven by a pulse width modulator which displays the RPM. Some of the nicer tachometers have a microcontroller (computer) in them and can save the history of the RPM and run a shift light.
(Why yes, I am an engineer.
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