Thanks for writing. First off, I'd remove digging out the sod with a sod remover; if you till up the grass, you'll likely have some resprouting as tilling doesn't kill all of the root system. If you don't mind using herbicides, you could also spray the grass with a weedkiller.
Once the grass is taken care of, I'd incorporate some compost into the garden (it'll do wonders for helping your new phlox get established). Then go ahead and plant, water your phlox in, and add some mulch over the top of the soil to help stop weeds and to keep the soil moist during times of drought.
See it step-by-step here! http://www.bhg.com/gardening/yard/garden-care/building-a-new-garden/
---Justin, Senior Garden Editor, BHG.com