Answer: There are several ways to do this.
You could rent a sod cutter and cut off the sod -- it removes the grass and its top roots and thin top layer of soil. This is very heavy work but it is fast. You can compost the sod so it does not go to waste.
You could use an herbicide containing glyphosate to spray the area and kill the grass roots and all. Read and carefully follow all of the label directions. This leaves all of the soil in place.
You could smother the lawn by covering it with newspaper topped with mulch. This method works quite well if you are starting with an essentially weed free turf area. It preserves all of the soil and also adds the composted lawn grass to the soil, along with the paper and mulch. These will break down over time to help feed the soil. To do it, first mow as short as possible and leave the clippings in place. Spread damp newspaper about five sheets thick over the area. Overlap the edges to exclude light. Top with a generous layer of organic mulch. If any weeds manage to emerge, spot treat with glyphosate. By fall, you should have a good planting area. Check the soil and see if you need to till, or not. Sometimes the area composts so well that tilling isn't really necessary and you can dig planting holes for each new plant. Otherwise, till the dead grass under and allow the area to resettle for a week or so before planting.
Keep in mind that tilling will bring weed seeds to the soil surface where they will germinate. Most new gardens have some weeds initially due to the "soil seed bank." Every time you till, you bring more to the surface. Mulching between your new plants will help limit weeds, but be prepared for some early weeding.
Good luck with your new plants!
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