Below is a picture of the first step. Just the perimeter grass of the bed needs to be pulled up. My trusty spade can be seen in the foreground.
Step 2: Cardboard is laid over top of the grass. A layer of organic matter is put overtop of the cardboard, in this case lawn clippings and fresh compost. Another layer of soil is placed over top. The idea is that the cardboard will work to smother the grass and then eventually decompose.
Step 3: Patience. Once your layers are in place you can really only plant shallow rooted plants until the grass is smothered and the cardboard layer has decomposed which will take at least several months. I cheated a bit to plant a lemon cypress, cutting through the cardboard. Below 2 pics of the bed one year later.
You can see from the first "before" picture that some plants have been shuffled around. Shannon gave me some rudbeckia and I added the lemon cypress which really glows in the winter time. I've grown some carrots at the apex of the bed for easy access for kids needing a snack . I'm quite pleased with the result of the new bed and found the "lasagne method" to be kinder to my body. I would recommend this method to others looking to eradicate grass in order to establish more garden space.