I found a set of wonderful sari/saree wrapping videos on youtube.
https://www.youtube.com/playlist?list=PL0B1F2FE35193AC5C

This one, showing a Kerala sari, and this one showing how to drape a sari in under two minutes are pretty much the basic drape I've taught in all of my classes. It's still my favourite drape and I find it works best with softer fabrics or a heavy brocade. The image above is me attempting this drape with a light cotton, my orange blockprint. As you can see it's not really falling right and I look a little frumpy. Still, one of the easiest drapes to look graceful in I feel.