A basso continuo part is made by the performer by creating (or "realizing") an accompaniment from a composed bass part by improvising harmony above the written notes. The chordss to be played are either determined with reference to the other written parts in the piece or else by interpreting numbers written by the composer beneath the bass part (known as figured bass).
The instruments used to play continuo parts vary and their selection is largely based on taste. In modern performances, the combination of cello (which just plays the bass notes) and harpsichord is frequently used, but in the Baroque period various other instruments were employed, including the organ and the lute.
Basso continuo was employed most often in the baroque period (around 1600 - 1750), though continued to be used in many works in the classical period (up to around 1800). Examples of its use in the 19th century are rarer, but they do exist: masseses by Anton Bruckner, for example, have a basso continuo part for the organist to play.
Modern editions of music originally written with a continuo part usually supply a keyboard part in which the harmonies are fully written out for the player, eliminating the need for improvisation. With the rise in historically informed performance, however, the number of performers who improvise their parts, as would have been done when the pieces were first written, has increased.