Harmony notes are the simultaneous combination of two or more sounds. The most common harmonies used in lead playing are thirds and sixths. Octaves are also used (although these are not technically harmony notes).
Thirds are any two notes that have an interval of a third between them. This interval can be calculated by counting up three notes from the lower note, including the lower note as the first of the three, e.g.:
Here is the C scale in thirds:
This gives a pattern on the fretboard as such:
Thirds: 2nd and 3rd String Pattern
Play this pattern up and down against either a C major or A minor chord progression, and memorize it. You can either use a pick, or the second and third fingers, as shown in the following photo.
For the key of C major, start at the 5th fret as marked. Thus you are starting on the fret at which pattern one is located. Practice playing this pattern of thirds in other keys, e.g., for the key of G, the pattern starts at the 12th fret (or in the open position) as does pattern one (you will find it more convenient to play down from the 12th fret, rather than continue up the fretboard).
Thirds can also be played on the 1st and 2nd strings, giving the following pattern:
Thirds: 1st and 2nd String Pattern
This pattern can also be played on the 6th and 5th strings, the 5th and 4th strings and the 4th and 3rd strings. In each case, firstly locate the root note for the key you are in. This root note will be on the lower (in pitch) of the two strings. E.g., here is the C scale in 3rds, on the 4th and 5th strings.