Fertilize in spring and again in summer and early fall. The particular turf you have will determine fertilization rates as centipede gets very little, st. augustine or zoysia a moderate amount and bermuda a little more. Use a product with a 3-1-2-or 4-1-2 ratio of nutrients. For bare spots loosen the soil with a spade (not turning the soil over, just punching holes and breaking it open a little. Then fertilize the area, spread compost about a half inch thick and water it in well.
The following web sites have lots more info on turf fertilizing in Florida:
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