An independent adoption works the same way a private adoption does, when the birth parents and the adoptive parents make an agreement that the adoption should go forward. There is no adoption agency involved. Independent adoptions are more direct than agency adoptions. The birth parents meet the adoptive parents. They then give the child to the adoptive parents (usually at the hospital when the child is born). They can also decide if they want to have contact with the child after adoption.
The law says the adoptive parents must be at least 10 years older than the child being adopted. If the child is already born, the parents can give the child to the adoptive parents during the adoption proceedings. The adoption proceedings usually take about 6 months to complete.