Admonish the Sinner
For this spiritual work of mercy the focus in not on What Would Jesus Do, but on What Did Jesus Do. You can easily see in the Gospels the variety of ways in which Jesus confronts people's sinfulness and admonishes them to do better. "Go and sin no more", "The man you are with now is not your husband." "You heap up burdens on others but do not lift a finger yourselves to help them." Over and over again we find Jesus calling people to task on what they have done wrong. Sometimes gently and sometimes not so gently, as when he drove the money changers out of the temple with a whip.
This is not to say that you should go around whipping sinners. But you are in fact called to admonish people's sin, to tell them that something they are doing is not in accordance with the Will of the Lord. It isn't enough to simply think, "Ah, I'm sure they will hear the message somewhere else." or "I'm sure they know the truth and there is nothing I can say to make them stop." With all that being said, you must be like Jesus when he did admonish people. Harsh words may be useful sometimes, but more often he used gentle words.
Ultimately to perform this spiritual work of mercy correctly you will need to put yourself in God's hands and seek to follow His Will. People don't like to hear that they have been sinning. Let God work through you to reach them, to help bring them home, but at the same time do not expect an on the spot conversion. It often takes time for people to internalize their wrongs and to come home.
Reconciliation
In this endeavor you must be an apostle of Reconciliation. As much as you admonish people for their sins you must also provide them a way to take care of those sins. And by the same token you must be a frequenter of the sacrament yourself. "First remove the beam from your own eye and then take care of the splinter in your brother's eye." Go to reconciliation regularly, at least once a month, maybe even once a week. The graces conferred in this sacrament will help you tremendously with performing this work of mercy.