Answer: You can chemically kill the grass with an herbicide such as Round-Up and then dig it out, or you can simply dig out all the grass and roots, lay down a weed barrier to keep it from resprouting (use either several thicknesses of newspaper or a commercially available permeable weed barrier), and cut holes in the weed barrier for your plants. You'll want to cover the weed barrier with an attractive mulch - either bark chips or decorative rock.
Either process will give you several years of attractive, weed-free gardening. Enjoy!
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