*worked out from piano*

B/G in this context = B note with left hand, G chord with right.

Bb/Gm = same idea, and so on.

so this song is a bit tricky ;) But basically, it's just a baseline C >> B >> A >> D for 
the main part of the song thusly:

Well there was a man,
C                B         A           D

lived in a shed
C           B           A            D

And so on. may not sound right at first, but i'm pretty sure it is.
You can play the  baseline with the your left hand and then add the
chords, embellishments, etc with your right.

Then for the other part:

When it rained, he felt so bad
C        B/G    Am          G


When it snowed, he felt just simply sad
C       B/G       Bb/Gm           A/ Gsus2