Keep St Augustine mowed between 2 and 4 inches. Dwarf types at the lower end, and coarse types such as Floratam at the higher end.
Apply pre-emergent herbicide. This will cut down on summer weeds.
If you have had insect problem in the past, treat with broad-spectrum insecticide. If you use a granular variety, water the lawn immediately after application to help get it into the soil. Make sure it has control for chinch bugs.
Don’t overwater. In the active growing season, St Augustine needs about 1” of water a week, from natural rainfall or irrigation. Too much water can cause fungus.
Apply fungicide (if needed). If you have had a fungus or disease in your St Augustine in the past or have quite a bit of shade in the yard, you should apply a systemic fungicide to prevent future outbreaks.