It depends on which product has been applied. You should always refer to the fertilizer manufacturers labeling instructions and precautionary statements. It is best to keep children and animals off the treated areas if you have any reservations.
Additionally, minimizing traffic on treated areas for the first 24-48 hours after a fertilizer application will allow maximum absorption of the materials to be effective. Most lawn fertilizers have no restrictions for lawn use. Fertilizers containing weed control herbicides or insect controls may require a pre or post watering treatment.