Correction as a leader is the same whether you are a Christian leader or not. First in a public setting you sit down and talk to the individual about what they are doing. if they do not listen you take someone with you, not to gang up on them but to make sure the individual can't get into a he/she said argument. If that doesn't work then the Bible states in Titus we are to walk away from them and pray for them.
The process of bringing correctness to a brother or sister is found in Matthew 18, "15 “If your brother or sister[a] sins,[b] go and point out their fault, just between the two of you. If they listen to you, you have won them over. 16 But if they will not listen, take one or two others along, so that ‘every matter may be established by the testimony of two or three witnesses.’[c] 17 If they still refuse to listen, tell it to the church; and if they refuse to listen even to the church, treat them as you would a pagan or a tax collector." ESV.
While the punishment seems harsh, today we call it tough love, you do it to be mean but to try and let the person see what they are doing not only to themselves but also to their friends. As a parent I know tough love is hard but I can also see where if you let everyone get away with what they want to do how it will bring down the whole. This is called co-dependency. I hope this at least helps to answer your question.