The grace note usually appears in the musical score in smaller print than the rest of the notes. The composer uses it to tell the performer how he wants a note to be played. When sight-reading a composition, the performer will see the grace note and play it as a short embellishment to the main note.
A 2001 study analyzed the timing of 11 grace notes in 45 different performances of a short piano piece composed by Ludwig van Beethoven. It found "significant differences" in the length of the graces notes, with two grace notes in particular played longer than all the others. The relative timing in the way a performer plays a grace note, researchers concluded, is explained by his "efforts to mimic the motor constraints of vocaliss and string players."
The acciaccatura grace note is usually played on the beat, though there is no rule that demands that. The word is taken from the Italian verb acciaccare which means "to crush," which is the desired musical effect of the note. It is meant to decorate the principal note, so its duration is very short. The precise duration depends on the tempo of the piece, with a faster piece requiring a shorter acciaccatura.
An appoggiatura grace note is usually written one step above the main note, although it can also be one step below. It must be played on the beat and in half the time of the principal note it is embellishing. If the principal note is three quarters, the appoggiatura may be played as either one quarter or two quarters, depending on which sounds better.