I don't think anyone answered Rowan's question, so lets have a go.

Melodies are easy, one note follows another in a fairly predictable way and most of us can sing along to a melody quickly -- millions do this in church or at a football ground every weekend.

Guitars and the like are providing the harmonies that give the song body. Suddenly there is more than one choice at every note in the melody, in fact there are often lots of choices at a note and each chord will give the song a different feel, jazzy, soulful, traditional, etc It is a lot more difficult to spot the chord (several notes) that gives the feel you want. Trouble is if you want say a traditional feel to a whole song your going to have to get the right chord at every change or the feel will break down.

There is nearly always more than one solution (set of chords), the sort of situation engineers and scientists hate but artists love. There is a song two of us sing at our folk club using completely different chords. We are both right the chords used fit the way we individually sing the song. The important thing is never to take the chords provided as the whole truth and nothing but the truth; you might need to vary them to fit your singing or the other guys singing fi you are accompanying.

Finger picking makes it even more complicated because often the choice of strings picked makes a basic chord into another, the songbook will list the basic chord but you know you can hear something different.

It does amaze me how some people can play the right chord first time, or get close first time and get the right one on the second verse. It does boil down to practice, practice, practice generating new pathways in your brain which collect the last few notes of the melody, the last chord played and the next note (or even a prediction of the next note) and workout a chord for you. I can't do it, but I don't practice enough.

Most embarrasingly I was trying to work out the chords for a song recently and ended up with a really complicated set which almost but didn't quite work out. My wife Sandra played along to the CD and went straight into D A G all the way through; did I feel dumb or what, I had assumed the song was in a different key and not bothered to check the melody. Maybe with another 50 years practice I'll be more musical by the time I'm 98.