How should a pastor deal with the lost sheep in his church. For example - members whose family are drug addicts or youth with a troubled past.

This is a problem every pastor struggles with and there is no simple solution to it. However, to the best of my ability, I will give some suggestions. But first, let us look at the key passage in scripture dealing with this problem in the churches:

Galatians 6:1Brethren, if a man be overtaken in a fault, ye which are spiritual, restore such an one in the spirit of meekness; considering thyself, lest thou also be tempted.
See All... Brethren, if a man be overtaken in a fault, ye which are spiritual, restore such an one in the spirit of meekness; considering thyself, lest thou also be tempted. Bear ye one another's burdens, and so fulfil the law of Christ. For if a man think himself to be something, when he is nothing, he deceiveth himself.

1. First, approach the problem spiritually. Even those who used to be where the backslider is will often look upon those who fail in the faith with condescending eyes. We must come in a humble manner; in the "spirit of meekness." And we must realize that except for the grace of God we would be in the same state or even worse. We are nothing and we must remember this fact when dealing with those who have gotten away from the Lord and church. Restoration is a job for the spiritual and there is no room for pride in the spiritual man.
2. Second, though not mentioned in this verse, we must approach the matter with prayer--for this will always be the way of the spiritual man or woman. Bathe the matter in prayer and seek prayer warriors to join with you. Saturate the situation with prayer before you act and your actions will have many times the effect.
3. Third, try to find some way to minister to the one who needs to be restored. In Galatians 6:2Bear ye one another's burdens, and so fulfil the law of Christ.
   See All..., we are to bear their burdens. Those who fall away from church are often treated as the enemy and therefore they usually expect this kind of treatment. They expect proud condemnations and attacks. But that is not God's way. Minister to them instead. That may be something as simple as a birthday card or a kind note. If opportunity opens the door, that may mean much more. Ask the Lord to give you an opportunity to bear their burdens; to minister to them. Then look for that opportunity in expectation. Finally, make sure you walk through the open door when it comes.
4. Fourth, after the prayer and ministry, approach them directly with the problem in a spirit of meekness. However, be much "prayed up" and let the Lord lead you as to how far to go and when to back off. Do all you can to leave the door open for further visits and conversations. Remember, it will not be your arguments or forcefulness that will reach them; it will be the conviction of the Holy Spirit and their submission to that conviction. If we push too hard too soon, we will get in the way of the working of the Spirit of God.
5. Fifth, be patient. Do not be discouraged because you do not see speedy results. Someone has said that the wheels of God turn exceedingly slow, but they grind exceedingly fine. God uses events in a person's life to force him to face his need for Him. I believe that if we pray and do our part that the Lord will providentially work the events of a person's life so that they can be brought to the necessary conviction and repentance. We are too ready to give up if the person does not turn around in a week or two. However, in most cases, it took the backslider a long time to get away from the Lord. Therefore, we should not be surprised if it takes some time to bring them back. Samuel told the Israelites (at a time when they turned from the Lord by demanding a king): "God forbid that I should sin against the LORD in ceasing to pray for you" (1 Samuel 12:23Moreover as for me, God forbid that I should sin against the LORD in ceasing to pray for you: but I will teach you the good and the right way:
   See All...). How many times have we sinned against the Lord by ceasing to pray for one who has gone astray. The parables in Luke Fifteen of the lost sheep, the lost coin, and the lost son, show us the effort that God expects from us in seeking the sheep who have gone astray.