Embellishments are created by involving the surrounding notes of chord notes. The example below from Czerny's Pianoforte-Schule Op.500 (1839) shows a broken C-chord embellished with the semitones below the chord notes.
Often the diatonic note above the chord note is involved as well, as shown in the example below from Montgeroult's Cours complet pour l'enseignement du forte piano (composed 1788-1812).
An endless number of combinations can be made with embellishment notes. Despite the fact that these embellishment notes in broken triads are very often found in written-out preludes, piano methods rarely provide specific exercises for this. Instead, one may find exercises where the principle of a lower semitone is practiced in a scale exercise, as in the example below from Adam's Encyclopédie du Pianiste Compositeur (1840).
Exercises for studying common embellishment patterns around a C-chord can be found here.