Your Grass is...Grass
The first order of business is to get rid of the grass, and there are a few ways of doing that. You can use a chemical grass killer like RoundUp (or an organic substitution, if you prefer) to kill your grass, then roto-till the area once the grass is dead and rake out chunks of grass and roots. RoundUp can take a few days or more to kill the grass, so if you don't want to wait, another solution might be for you.
You can chop the live sod out (and maybe transplant it to another area of your lawn) and till the ground beneath to soften the dirt. A sod stripper can make the grass removal process easier and helps to save soil, or a sharp shovel may be used, but that can get kind of difficult if you're working a large area. Sod also makes a good addition to the compost heap.
You can also hack up the dirt and sod with your shovel, breaking up all the clumps of roots and grass, and turn all the dirt over. This method will require some additional weeding as your garden grows because you're not removing the plant seeds, but it carries the benefit of organic material (roots and plants) that will decompose and enrich your soil.
Once the sod is gone and the ground is tilled thoroughly, you can add soil amendments if you need to. If amendments aren't necessary for the plants you're growing, the digging part is finished. This is the time to add a border or edge to your bed if you'd like. If not, you're ready to start planting.
After creating your bed and working with it for awhile, unless you've been meticulous you'll likely to find weeds starting to pop up. Here is a quick video with some simple and earth friendly solutions: