RCVN How does singing work? I think I might be out of tune, but can't find a tuner..
I should be the last person trying to answer this...
I can only really sing in unison with whatever I'm playing on guitar (E.g. playing a G and then singing in pitch with that note). Harmony, (or harmonizing) would be singing a 3rd or 5th (note) relative to that root note you'd be playing.
I'd heartily recommend learning a song that you know well - I started with nursery rhymes (come to think of it, that's about as far as I got). Row yer boat is useful, because it uses most of the major scale.