Most importantly, they begin their walk in their new found freedom. Encourage them to immediately read their Bible and to attend church. They must serve Christ to continue their freedom. Never be afraid to pray for someone's deliverance. When you are secure in your life in Christ and Spirit-filled, the enemy will not be able to resist the commands that you make in Jesus's Name.
Nothing can keep a person who wants to be free from going free.
Since the person that was bound participated in their own deliverance they will be able to resist counterattacks by satan. They know that they too have authority through the Name of Jesus and their relationship in Christ. Encourage them to exercise their authority and to resist the enemy, and he will flee from them.