Hey Orlonater!
I'm not 100% sure exactly what you're asking but I can give it a shot. If you had problems matching the written music to the chart, here's how it works.
Here are the first 4 harmonic notes of the melody (G, D, F# & E) marked on the harmonics chart:
I think the chart makes it difficult to make out exactly where to find them, but I play the notes roughly on the frets, meaning 5th and 3rd on the G-string, 4th on the D-string and 3rd on the A-string. You might have to adjust your fingering just slightly for the last two to ring out properly. Pick near the bridge for a clearer sound.
Anyway, those were the first four notes. The next phrase uses the same positions, just a string lower, like so:
Nearly the same again a string lower for the next phrase, only move up to play the B and E harmonics at 7th and 12th frets, respectively, on the E-string:
That was all the harmonics in the first bar. I hope it helps -that should get you started, anyway.