Digging up a patch in your yard for a garden can be a traumatic thing for any lawn-enthusiast. Just ask my hubby. All of the years of lawn care and maintenance are about to be "defaced" by a shovel. I know he was worried about where to put it and what size to make it. He is one to second guess things and put decisions off until the last possible millisecond. I am much more decisive. Once I make up my mind, it is made up. Don't ask me to change the plan or do something entirely different- I've already visualized it and that's how it will be. He's a trooper to put up with me... and vice-versa, I might add. (LOVE YOU HONEY!)
We (And by 'we' I mean 'he'. I had to take the pictures you know.) started by putting 4 stakes in the ground where the corners of our garden would be. We measured the sides so they were equal, then measured the diagonals. If your diagonals are equal, the garden is square.
Then, run a length of string or twine around the 4 stakes, winding around each stake. Mark along the string using spray paint or a line of pulverized lime. Remove the stakes and string.
It isn't necessary, but at this point, you may want to remove the sod (grass) with a sod kicker or shovel (wear gloves if you use a shovel). The excess sod can be used to fill in bare spots in your lawn (lay on bare spot and water daily) or it can be broken up and added to a compost pile.
Now you can begin digging along the lines you painted. Dig up large chunks of the ground and, if you haven't removed the sod, turn the chunks over so the grass will break down. You may have to take a shovel or hoe and break the chunks up further to help them dry out more.
Once the dirt is sufficiently dry (which can take some time), you will want to till the garden up with a cultivator, tiller or disk attachment on a tractor. You can also add lime (to help the grass break down and make the soil less acidic), fertilizer, manure, sand or compost before you till the soil up. You can check with your county's extension office to find out what to add to your local soil.