A digital multimeter will often use a delta sigma ADC. The way it ultimately detects voltage is with the electric field of electrons on the gate of a field effect transistor. Basically, the electric field increases in strength the higher the input voltage(more electrons in the same space), and the electrons on the gate repel the ones that are trying to get through the transistor.
The simplest multimeter is the electromechanical kind the others have covered.
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