Last year I put in about 500 sq' of garden on top of the grass. I was working out of town so I was very rushed and got a late start. On some sections I laid out cardboard, on some I put lumber down to smother the grass, and one bed didn't get anything because I didn't have material.
I wet the cardboard at times, but pretty much just let it all sit for 3 weeks (late start). I then got several yards of
compost and used it to build my beds. I picked up all the lumber and put down about 3-4" of compost for each bed; some on cardboard, some on smothered grass, and some right on the grass. After 3 weeks the smothered grass was starting to die out.
I then put down weeper hose on the beds and covered all the beds with black plastic I got from Home Depot. The plastic was 10'X100', so I cut it in half and laid it out 5' wide over my beds. I used an edger to cut the grass beside the bed, tucked the plastic into the trench, and stamped it down to secure the plastic. I let that sit for a week (with watering) and then planted my garden through the plastic.
Most of the 'soil' I had was an inch or two deep over gravel where there had been car parking, so I wasn't working with much. My garden did surprisingly well for such crappy soil, though I did use compost tea on it fairly regularly. When I planted I found the beds were a worm paradise, with 2-3 worms found in every trowel hole. About a month after I planted the garden really took off and I think that was at least partially due to the grass finally giving up the nitrogen.
Personally, I wouldn't remove anything, just cover with cardboard, add compost, put in weeper hose, then cover with plastic. I didn't have to weed at all, thanks to the plastic mulch.
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