What I did was really really simple: Repetition
Keep repeating one section until I find the right sound. I find the bass note that is used in the song, then I try and find a chord based on the bass. You can alomst tell if something is a major or a minor when you hear it, kinda. For example, based on the bass, I then listen to the piano/organ chord for a "base sound" (major,minor,diminshed). After that is established, I try to "phatten" the chord. But, a song like this, there is a lot of chords and you can't stay on one chord for too long.
Why are you asking? Are the chords horribly wrong? lol
Also, what process do you use? Maybe, I can adopt it...