No Grass Here
In order to get rid of some grass in an area I'm not going to plant this year, I laid multiple layers of newspapers down - laying them like a brick wall. Overlapping in multiple layers with no direct pathway the grass can take. I then laid 4 inches of wood chip mulch down over top of the newspaper to hold it down and add another layer of material the grass will have trouble penetrating.
This is a ton better for the environment than spraying anything. It gets rid of some paper (it decomposes slowly over a few years) and it uses up some wood chips.
This should get rid of the grass this year and next year when I want to plant in this area, it should be good soil down there with no surviving grass.