try to work out hearing your intervals. 7-3-6-2-5-1 or any portion of that is moving in perfect 4ths which is usually easiest to identify. others would be moving a 5th, a 2nd or a 3rd. It sounds complicated but its easier than you think. You can identify when the chord moves, this is just getting used to hearing how FAR it moved in either direction.
once you do that, listen for the chord quality (major or minor or diminished first, then all the other stuff). for non-over-the-top-complicated songs, this helps you tell which interval it is.
For example all of these move in 4ths, but there is a difference in the combination of chord qualities
7-3-6 => dim - min - min
3-6-2 => min - min - min
6-2-5 => min - min - maj
2-5-1 => min - maj - maj
5-1-4 => maj - maj - maj
now when some folks wanna get tricky, they change chord quality, but you should be able to figure that out at your instrument.
after that there's tricky stuff, like chords outside the diatonic scale that arent always diminished chords. you just have to be at your instrument, find the root note, then work out the chord quality. after a while your ear should be able to recognize them. its like being able to spot your friend in a crowd of people.