Hi Don,
Ah, song accompaniment, how many ways? I guess it depends on the song and the singer. I'm no expert by any means but I'll try to tell you a bit of what I do. I believe you're probably playing an english.
First, a song is a song, so the words are the most important part, you're telling a story, the accompaniment should compliment the story.
From sheet music I start from scratch. If there are recordings I usually listen a few different versions. Often I'll record into a program called "Cool Edit" with which I can create a waveform. Then I can loop the whole song or parts of and play along. I can change the key too, sometimes it sounds like chipmonks. You can do heaps with these sorts of programs.
I'll decide what key is suited to my voice then I'll usually learn the melody. Then I'll learn the chord progression using a different inversions and with this process I'll start to get a feel for the song. This can take a few days or a couple of weeks. I'll play chords along to a recording over and over and over. I found a great way to learn chords ( 3 to 5 notes usually) was to play along with 12 bar blues practice tracks, there's heaps on the net in all keys.
I do like a simple accompaniment but sometimes a fuller sound is required. Mostly I sing along to chords or parts of chords and the voice provides the melody. Sometimes I just sing to the melody. With instrumental breaks I'll usually try put the melody over chords or parts of chords but I don't think the chords have to be continuous. Sometimes the low note chords will swamp the higher phrased melody(solution,fewer low notes) but sometimes the melody can go underneath the chords. This happens a bit in Honey Pie. To get a rhythm during singing I'll often vamp on the off beat, like in bluegrass. Sometimes I'll hold one or more notes of the chord and vamp the other notes. This happens a little bit in Rainbow just before the chorus. Other songs I'll use heaps more vamping and vamping sometimes causes the bellows to add to the rhythm.
Some songs come together quickly, others take a while. Listening to different recordings I often pick up little bits to use. With Cool Edit I can slow them down to figure them out. Songs like Honey Pie with lots of chord changes I find more interesting, they work out their own accompaniment.
Thanks for starting this post , it's made me think a little about what I do. And still learning. Yes the site is pretty much tune orientated. I've started scouring the videos hoping to encounter others accompaniment styles but haven't found too much yet, nothing that's not traditional. Yet in it's heyday the concer was often used for contemporary and popular song.
Cheers Steve.