As people have noted it depends if your talking IDing notes and chords out of thin air or relative to another note or chord.
The thin air one is tough, but can be done with practice or if you have perfect pitch or people who can ID chords and notes like the rest of us do color. It is actually a curse, someone people who have this have trouble playing in different keys other than the original song, because to them it is like watching a movie where all the colors are backward (red is blue, etc) that said over time (20+ yrs) I have noticed when picking songs off the Bluegrass station that I can get the key/chord on the first try pretty often, but definitely not 100%.
The ear train as "relative to another chord/note" is what I think of as the classic ear training, and here it can be taught with a little less time. When I took an ear train course at a Guitar workshop, they basically would teach you an interval or progression and have you associate it with a popular tune example 1st to a 5th - opening notes to Star Wars, 5 to 1 Flintstones, 1 to minor 3rd - heartbreaker (Led Zeppelin) . Here is a link to others http://www.theory.mikesparksmusic.com/files/Download/The%20Intervals.pdf
Chord progressions the same thing I, IV, V pretty common, I, V, vi, IV - dont stop believing, Journey and countless others... here is an Australian comedy group showing that progression is like 100 songs- https://www.youtube.com/watch?v=oOlDewpCfZQ