Since different instruments' timbre is composed of varying amounts of harmonics that change over time, with respect to a base tone, additive synthesis emulates this behavior similarly by creating a different amplitude envelope on each harmonic, as well as adding non-harmonic artifacts aiming to result in a realistic timbre recreation.
Usually this involves a bank of oscillators tuned to multiples of the base frequency. Often, each oscillator has its own customizable volume envelope, creating a realistic, dynamic sound.
A classic analogue additive synthesizer was the Synclavier.