St. Augustine is a heavy feeder. It needs at least one pound of nitrogen per 1,000 square feet, per month to stay evenly green. Less than that, and you get irregular growth and coloring. More than that, and your lawn will produce very lush growth that is open to pest and disease problems.
One problem that St. Augustine Grass can have is iron chlorosis, or lack of iron. This most frequently occurs in alkaline soils (pH of above 7.0). The optimum pH range for St. Augustine is 5.5 to 7.2. The pH of the soil affects nutrient uptake, not just for iron, but for a wide range of macro and micro nutrients in the soil. With St. Augustine, if you are having growth or color problems, try testing the pH before adding anything to the soil.
If the pH of the soil is too high, you can add sulfur to the soil. Lawn and garden centers will have products specifically for lawn care. If you have corrected the pH and the grass blades are not dry, but are a yellow color, that is a sign that you need to use a foliar iron spray on the grass. (Foliar means it sticks to and is absorbed through the plant leaves.
Your local state funded university is usually a place that does soil tests. The cost is also much less than a private laboratory. Sometimes, a local garden nursery can also test your soil when a particular plant has problems.