Curing soap does two main things. First, it allows the soap to dry out and harden so that it will last longer. Second, it allows it to fully finish the saponification process so it is the mildest bar of soap possible.
We allow our soap to cure for a full 6 weeks, but if you are super anxious you can use it at 4 weeks. The soap is safe to use from 2-4 weeks cured, but it will not last very long if you do.
To cure, you want to place your soap in a place out of direct heat or sunlight where it can get airflow. Do not put it in a sealed container. When we first started making soap, we placed the bars on the wire racks in our closets. Do not place it on metal or on finished wood (put a towel down first if you want to use that). If you are placing the soaps on a solid surface, you will want to turn them at least once a week.
This is a video Emery did several years ago. We no longer have the 3 pound logs available for sale, but the other information is good.