Apply granulated fertilizer to a dry lawn and wait at least 24 hours to water it. An exception would be weed and feed, which should be applied to damp grass.
Fertilizer should be applied in the spring and fall when the lawn is still growing. Plan around the local weather forecast to avoid top dressing the lawn during rainy weather. Watering the grass right after fertilization washes away the product, but a light sprinkle does not harm it. Too much water can wash plant food into the local water system and cause an environmental hazard. Read the instructions on the fertilizer package for more specific instructions.