How do you write a piano arrangement using chords? Which chord to use?

I can play the piano pretty well but always use sheet music. I have taught myself, and I know that there is a "methodology" (for want of a better word!) to which chords you play for which notes. Is there somewhere I can find out more information about which chords are which and which notes they sound best with? I would like to write some piano arrangements and am fine with the melody (right hand) but just don't know where to start with the left hand!