Left click on the edge you want to add a point to. Then left click
where you want the new point. It seems to be picky about what "on the
edge" means, though.
It's not really picky at all - just click *inside* the polygon near the
edge you want to add a point to. If you have 45 degree enforcement on,
it might be really picky about where a new point is allowed to go, but
then it's supposed to be.