Put on work gloves and spray paint an outline of the area where you wish to plant the St. Augustine grass.
Use the shovel to dig up any grass or plants in the area you outlined with the spray paint, and dig out a couple of inches of earth below if you have in-ground sprinklers so you don't bury them, or if you want to make sure your lawn is level with--not taller than-- your driveway or walkway.
Rake away any rocks or other debris from your work area.
Spread an even layer of St. Augustine fertilizer over your surface.
Spread the sod across the area you wish to cover so that the edges of the pieces of sod are flush.
Water your lawn so that it is damp but not soaked, as too much water will drown your grass. The general rule is one inch of water a week, broken down into two or three watering sessions a week.