Here's a very amateur video I shot yesterday of how we actually plant rice in California. We do all of our land prep (i.e. disking, leveling, spreading compost), then flood the field. Next we load pre-germinated seed into a crop duster and fly it onto the field. That's what the video shows. You can actually see the seed hit the water. The planes all have GPS navigation systems so they know exactly where to drop the seed.
Those are our pet ducks in the foreground.