Thanks, all. I used a combination of methods - digging up one square foot at a time with a shovel in those area where I wanted to plant right away or if the soil level was too low, smothering with newspaper, soil and compost to create a raised area or to level out a slope on those area that I was able to leave over the winter, and using roundup in just a few spots where I wanted to kill the grass, but I was not ready to plant yet and did not want the bare soil to erode.
Renee - do you have relatives in Sacramento? You are welcomed any time!
Hetty - a few inches here and there is all you need to eventually end up with none.
My original goal was just to create this small raised bed for a peony plant that I bought a couple of years ago. At the beginning, I had no intention of tackling the whole lawn because I thought it would be too daunting.
He was even kind enough to move them over to my yard for me. If you look at some of the rocks, you can see where the water line was. 
