Mow the grass short, lay down about 10 sheet thickness of wet newspapers and cover it with shredded bark. You may have to pull or dig the occasional weed....but it will kill the grass.
Linda C

Using this method means that you can plant when the grass has died, which probably takes at least a season.

Try for an "airtight" cardboard layer (lots of layers, lots of overlap):
Grass is sneaky.

If you want to plant sooner, cut the sod & pile it in a compost pile, then add new compost/gardensoil/mulch.

If you use stones, you'll have grass (*weedy* grass!) slinking up between them for the rest of your life.

I just know this.

sylvia

My back lawn was full of weeds. This spring, I covered it with all kinds of papers, cardboards, corrugated boxes, cereal boxes, etc. & junkmail, catalogs, magazines and newspapers.I used the entire tickness of the newspapers, catalogs and a few layers of cardboards, overlapping them, wet them down then I spread barks on top. I replenish the papers as I collect them. Cardboards breakdown much faster than newspapers. I only had problem with dock growing through twice. I just dug it up. Everything else is dead. This fall I am going to plant miniature Daffodils and tulips there. :-)