It used to be that when I wanted to eat away at the lawn a little more and make a new bed for planting in, we'd rent a sod cutter and remove slices of grass (and/or weeds) with their roots, and then dig in compost until the soil was right for planting in. Now I'm using the no-dig sheet composting method, which is easier on the back and works just as well.
Here's how I created a new shade to sun bed for small trees, shrubs and perennials last September.
Finally the entire shape of the bed was laid out. Time to plant!
I could put my larger plants in right away because the soil underneath was good. If you have solid clay you probably want to wait until you've created some new soil above the paper.
This counts as a Grow It Eat It bed because I put in a fig tree and a pawpaw. If I want fruit on my pawpaw I'll need to put in another one... somewhere. Not sure where yet. The other plant you see is a bayberry.
Next I started the layering process. On top of the newspaper I spread some compost and, as the autumn progressed, fallen leaves and grass clippings. Lots of materials could go to make a sheet composting bed (see page 3 of HGIC's Backyard Composting fact sheet for more information); if you are planting in it right away as I did, you need to use already finished compost and keep fresh materials like grass clippings away from the new plants.
Later last fall I put in a few perennials and some small bulbs, and I've continued to plant this spring, but it'll take a while to fill up the bed. Meanwhile I'm mulching and I'll add more compost in the fall along with some leaves. Last fall's materials have decayed into a loose rich soil. I have had to pull out a lot of weeds... and I have a large patch of columbines coming up in the middle that I didn't plant.
The best thing about this method is how quickly you can move from imagining your new bed to having it, without back-breaking shovel work. I'm doing part of my vegetable garden this way too, but haven't had time to accumulate materials to build it up yet. Next year!