I turned a couple pieces of my lawn into flower beds very simply with no digging:
Lay down several layers of cardboard or a bunch of layers of newspaper, water thoroughly again until the paper is wet through
Put down several inches of a good soil/compost mixture (at least 3" if you are putting in plants, at least 4-5 inches if you are planting seeds) and water again.
Plant into it, digging holes through the paper if you are transplanting plants into it.
By next year the paper will have disappeared as well as all the grass and you will have beautiful deep soil.
It helps to put edging around it so the surrounding lawn doesn't grow back into it.