What is the best way for someone with a minimal amount of music theory knowledge to figure out the chords used in a song? I've used Chordify (chord recognition software) if someone hasn't published the chords for a given song already, but I'd like to be able to do this myself, particular since the software can only really handle basic chord progressions and tends to be inaccurate even then.
In a given key, there are basically 3 main major and three main minor chords found in the underlying harmonies. Majors are I, IV and V. Minors are ii, iii and vi.This will translate in C to be C,Dm,Em,F,G and Am.Those chords will cover many, many songs and tunes from many genres, in Western music.
First to establish is the tonic - the key chord of a piece. This is usually the last note/chord of a piece, and the chord that feels like the tune has come to a natural end on, even if it's only at the end of a line.That gives chord I. From there it's easy to work out the other 5.
Assuming the tune is on one chord,a major, when the change occurs,and it's another major, there's a 50% chance of getting it right first time. If the chord is C and a major change comes up, then the choice is F or G - 50%.
The same for minor to minor, and with a maj. to min. (or vice versa), the chances are 33%.
With experience, you'll go straight to the next chord pretty often. Another thing to remember is that a particular chord is quite often preceded by its fifth. As in if you're on Dm, there's a good chance the next chord may be a G. This is seen often in the jazz ii-V-I idea.
All this works best if one counts up, alphabetically, to find I,ii,iii etc., but bear in mind there are sharps or flats in most keys that will need applying.
To find 'odd' chords which don't fit diatonically within a key is another game, but I'll leave that for now.
I know how you feel Rich. Genres like jazz and gospel tend to use a lot of "weird" chords that don't fit into whatever the home key is.
Knowing the bass note of the chord is crucial in my opinion. Sometimes people can't hear it and that makes chord identification difficult. If you can hear it, then it gives you a ton of info. Let's say the bass note is C. This means that C could be the root, 3rd, 5th or 7th of the chord. Although we could say it could be the 9th, 11th or 13th, it's not as likely. Here are possible chords depending on what position C is within the chord:
C as root: C major, C minor, C7, Caug, Cdim (there are obviously more, but these are the foundational chords based on C as the root)
C as the 3rd: Am/C, Ab/C, Adim/C, Abaug/C (and any variation with 7th like Am7/C, etc)
C as the 5th: F/C, Fm/C F#dim/C, Eaug (C would officially be B# in this case)
C as the 7th: DbM7/C, Dm7/C, D7/C, D#dim7, Dm7b5, etc
You can see already for just a single note how vast the possibilities are! It's not impossible to list all possibilities, but it's also not easy to do so. There is no substitution for understanding commonly used chord progression as posters above had mentioned, which means there's not really any way of getting out of knowing and understanding theory unfortunately unless you have a stellar ear.
Some additional info: Generally, if the chord is not major, minor, aug, dim, dom7, maj7, min7, min7b5 or dim7 then it will typically use some sort of chromatic approach. This is where an "in key" chord is approached from a semitone above or below. Upper structure chords (US...see http://en.m.wikipedia.org/wiki/Upper_structure) can be used in this way and are used like crazy in jazz.
It could also be a passing chord generated by the cycle of 5ths. For instance, the E major chord can be used in the key of C major as a passing chord to the VI chord (a minor). Why? It's satisfies a typically cycle of fifths progression, which are simply a series of V to I progressions.
Hope this helps, if it wasn't too confusing :)