Harmonized scales/melodies are a great technique many bands like the Eagles, Pink Floyd and the Allman Brothers use to great effect.
Initially, I like to teach this concept predicated on the major generated modes, which are: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian. The first step is to learn those scales...
Once you've done that, I recommend you use either a loop pedal or recording software to do the following: First, record yourself playing a G major scales (up and back ) then, when you play it back, play a B phrygian scale over it, then do the same with a C Lydian scale and a D Mixolydian scale. These three harmonies, 3rds, 4ths and 5ths will sound the most familiar but still really interesting.
Next, let's harmonize a simple, diatonic melody: well go really simple here and use “Ode to Joy”. Play the first part of the melody in the G major scale shape, the notes are: B – B -C D – D – C- B – A – G – G -A – B – B – A – A. If you convert the intervals of the melody into scale degrees, you have: 3 – 3 - 4 – 5 – 5 – 4 – 3 – 2 – 1 – 1 -2 – 3 – 3 – 2 – 2. (Which, in this example are both the scale degrees AND the intervals, this will not be the case with the harmonized scales)
Now, to harmonize the melody notes from the G major scale in either 3rds, 4th or 5ths simply use the same scale degrees in the harmony scale as you did in the original melody played within the G major scale.
Ex) To harmonize in 3rds, use the B Phyrgian scale and the degrees are the same as in the G major based melody – the B is harmonized with the D and the C is harmonized with the E etc.