@LucyG Bless you for wanting to help and the Bible clearly states that we are to help them and Jesus himself gives us the model for confronting sin in a fellow believer.
Hebrews 3:12-14 Take care, brothers, lest there be in any of you an evil, unbelieving heart, leading you to fall away from the living God. But exhort one another every day, as long as it is called “today,” that none of you may be hardened by the deceitfulness of sin. For we have come to share in Christ, if indeed we hold our original confidence firm to the end.
Matthew 18:15-17 “If your brother sins against you, go and tell him his fault, between you and him alone. If he listens to you, you have gained your brother. But if he does not listen, take one or two others along with you, that every charge may be established by the evidence of two or three witnesses. If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector.
Sean has given great resources for when the situation involves doubt. Here is some guidance when it is unrepentant sin.
Whatever you do should be done with gentleness and compassion. Pray and seek the guidance of the Holy Spirit. Circumstances will vary greatly, but for a person who is unyielding and choosing not to repent, expect defensiveness and even anger. Let them know you will be there for them when they choose to deal with this sin, but sometimes, like with an addict they have to fall very far before they are willing to let it go and give themselves back to God. In those circumstances our best tool is continued prayer for that person.
If the person is truly feeling shame and guilt, chances are their heart is ready for repentance even though they may not really know it. That shame/guilt may indicate the convicting work of the Holy Spirit. In these circumstances I think a powerful tool is to ask them to remember and share what brought them to Jesus initially. What was that like? How did that feel? Have there been any powerful moments where they felt God’s presence/closeness? What do they feel now? Why are they choosing where they are now with where they were before in their closeness to God? Do they sincerely desire to know that closer relationship with God again?
Remind them that there’s a vast difference between believing in God and believing God. And if they truly believe then they should take God at his word when he speaks of forgiveness. There may still be consequences for their actions they will need to contend with, but they do not need to carry the burden of guilt and shame with them. If they themselves had a child that sinned against them, wouldn’t they want the child to know the fullness of their love and forgiveness after the child confessed and apologized?
Remind them also that we are ALL broken vessels in need of restoration. We all fall short. We all fall down. It is a far worse predicament to not get back up, to let their hearts become hardened and inured to the sin.
Listen to this person. Pray with this person. Love one another as we are commanded to do. Your gentle ministrations may be exactly what then need, whether they are willing to admit it or not. God bless.