To kill the lawn, I spread of thin layer of manure and compost over the grass and then covered the area with black plastic.
After about a month the grass looked sufficiently dead. I rented a rototiller and tilled in the lawn, then removed the spray irrigation lines and extended a drip irrigation line into the new garden.
I had a load of wood mulch and a few small boulders delivered and placed in the garden. The boulders provide a little bit of interest in the spring when there isn’t much blooming, and they are also very popular stepping stones for the kids that walk by.
I’ve added to the garden each year but I still have gaps to fill in.