When it comes to making a garden out of something that is not a garden, you have a few options. You can rototill it, but honestly that takes forever (at least three passes for sod) and is bad for the soil microorganisms, who get too churned up. Plus you always bite off more than you can chew with a rototiller or god forbid, a tractor.
You could go the no till method, but unless you are swimming in giant piles of compost and woodchips and hay, you are unlikely to be able to make a large enough garden without a prohibitively large budget.
The third option, the middle way, is the shovel. Oh, the shovel. It's pointed snout, judiciously sharpened with a file, plunges down through sod and willingly severs roots. The long handle keeps you from stooping, and the action of flipping each load maintains soil structure while burying the sod down deep enough where it mostly won't grow back.
Today I shoveled over a section of existing garden. It was an area of incredibly crummy soil that broke my shovel five years ago, and I finished turning it with a pick axe, a grueling process that took hours. It is still working its way to a reasonable garden soil, and this year's heavy application of compost should help tremendously. But for now, the flipping action of the shovel helps by increasing the organic matter down deep, as each load inverts the compost spread last year with the clay eight inches down. Spread more compost on top of that, and you are well on your way to a soil that will reliably grow good vegetables, provided you fertilize and amend as well (more on that later).
In many of our other garden beds, we simply use a broadfork to aerate and then spread and cultivate and rake. But if you are starting out, or if you are looking to improve a soil dramatically, go with a shovel. You won't regret it.
My blog has evolved into a series of short essays on the nature of entrepreneurship, craftsmanship, and their overlap. If either of these topics is something you think about, you will probably like this.