Updated: Aug 20
The first step is to hear the "home chord", referred to as the "1" chord. Do this by listening to the last note played or sung in any major section of a song, for example the end of a verse or chorus. Sing that note on the word "ONE"
The rest of the chords are found through their relationship to "1", so when you hear a chord change, you can sing the root note on a neutral syllable, then walk up a scale from "1" to that note. Ex... 1, 2, 3, 4, 5 - "Aha! it's the 5 chord!" The root note is usually played by the bass player, or instrument/voice with the lowest range.
Over time you will be able to hear this chord change without having to walk up from 1 - you will start to associate that change with a specific feeling.
Start training your ear with two chord songs, like the Hank Williams song, Jambalaya using just the 1 and 5 chord. Listen to the bass line and just recognize when you hear ANY change, before worrying about what that change might be.
Once you can recognize simple chord changes between the 1 and 5 chord, sing the chord changes on the number "1" and "5", then move to songs that use the 1, 4, and 5 chords. Then add the 6. Build your harmonic vocabulary from the fundamentals, and eventually you will be able to hear even very challenging chord progressions in jazz standards or classical symphonies.
Here is a sample grouping of songs by their harmonic function you will see that it gets progressively more challenging.
I teach an elective at music camps that guide people through this process. Check out the lesson above.
Here are the resources I mentioned:
My YouTube Channel - Please subscribe, it's a free way to help me :)
This is the class I used to run - It's what I'll consider doing in the wintertime!
And Here is Andy Mullen's channel, the Gordon's music learning theory specialist who created sing along videos for tonal/rhythmic acculturation