The first thing to do is always practice scales. Claire de Lune is written in Db major, so always practice the key of D flat prior to practicing the Debussy's piece.
By practicing scales, you learn the language of music. In a short amount of time, you will no longer see just notes on the page, but rather also patterns and chord progressions.
Apropos your question regarding learning melodies involving chords:
If you haven't already, I'd recommend playing Bach's Prelude 1 in C Major. It is all broken chords. When you practice it, make sure you stop on each measure and label the chords. The point o
Block the chords (play the broken notes simultaneously), and then play them as written (i.e. broken and arpeggiated).
You will notice that Bach was using ii-V-I progressions way before they became a staple of Jazz music :)
- the first chord in Bach's 1st Prelude is a C major triad
- the second chord is a D minor 7
- the third chord is a G7.
- the fourth chord is a C major.
In the C Major scale: C is the 1st note, D is the 2nd note, and G is the 5th note.
So we have a I-ii-V-I progression at the very beginning of Bach's Prelude 1 in C Major.
I recommend learning the Bach Preludes. Bach was way ahead of his time. Most of the chord progressions that are widely used in jazz and rock music can be found in Bach's music.
Debussy is also fascinating. Miles Davis was heavily inspired by Debussy. I'd recommend learning Debussy's suite Pour le Piano if you want to dig deeper into an understanding of chords. Many of the chords used in that suite are straight up jazz chords. The last 6 measures of the 1st part (Prelude) are incredibly beautiful i.e.
- A minor
- E minor 7
- A minor
The 2nd part of the suite Sarabande is almost all exclusively chords. And the sonorities are fascinating.
The best way to learn chords is to learn scales inside and out. Chords are after all just scale tones played simultaneously.