You may have heard that this isn't possible. Don't believe those advertisements that want you to spend money on their products. Organic lawn care can be easy, and it certainly is a lot safer than chemical based lawn care. When you spray anything on your lawn and then walk on it, the chemicals end up in your house. They can also end up in you as you inhale the spray, or pick up your shoes that have chemicals on them.
Children are even at greater risk because they put things in their mouths.
But never fear you can have a safe lawn. The first step is to pick the correct grass. Different regions need different grasses. You're looking for a drought resistant, high growing grass. I recommend talking to your local garden expert try the county extension agent or it's equivalent.