This short video shows some simple steps to easily create a harmony for your melody, whether the harmony is for a vocalist, a piano or an accompanying instrument.
To find the high harmony, start with the melody note and move 2 scale notes up. The low harmony is the melody note but 2 scale notes down. For example, if your melody note is an E (in the key of C), your high harmony is a G, your low harmony is a C. You can use either the high harmony, the low harmony or both harmony notes together with the melody.
If the high and low harmony notes are played together, they form a chord with the melody note, so adjustments may be necessary if the harmony forms a diminished chord (which may sound too dissonant). Try lowering or raising a harmony note to avoid this.
Check the harmony notes against the chord progression. In the video, the low harmony note had already been lowered a tone to avoid a diminished chord. This turned the harmony from a 3rd below the melody to a 4th below the melody but this clashed with the chord progression so the low harmony was lowered another scale note, which then made the low harmony a 5th below the melody which fit with the chord progression.
Also note that the high harmony can be played an octave lower, and the low harmony can be played an octave higher. This turns harmony in 3rds to harmony in 6ths.
All this is demonstrated in the video below.