The best time to start leveling your lawn is in May, when your St Augustine is actively growing. To fill the depressions, use a mix of half sand and half potting soil.
If the depressions are shallow, spread the soil mix over the low area to a depth of about 1/2 inch. Use a broom to brush the grass so the soil mix falls down to the soil, and then water. Allow 3-4 weeks for the grass to root into the new soil and then repeat. You might have to repeat this cycle several times, but you don't want to apply more than about half an inch of soil at one time, because you then risk smothering the grass.If the depression is more than about an inch deep, use a spade to lift the turf off the low section, fill the depression, replace the turf, and water.