According to Scripture, Christians can only address sins in others who are within their local church or assembly. Every church in the Bible was an autonomous church with elders and deacons. However, all the Christians within that church were part of the same spiritual family.
So if a brother or sister were sinning, anyone within that church could approach them and try to put them back on track. With love, meaning you do not make excuses for them, or allow them to make excuses for themselves. Here is one very pertinent Scripture:
Brethren, if any of you do err from the truth, and one convert him; Let him know, that he which converteth the sinner from the error of his way shall save a soul from death, and shall hide a multitude of sins. (James 5:19,20).
This corresponds to another passage in Hebrews 12:15,16: Looking diligently lest any man fail of the grace of God; lest any root of bitterness springing up trouble you, and thereby many be defiled; Lest there be any fornicator, or profane person, as Esau, who for one morsel of meat sold his birthright.
When it comes to someone who has sinned against you personally, then there is a distinct procedure which must be followed as given in Matthew 18:15-17:
15 Moreover if thy brother shall trespass against thee, go and tell him his fault between thee and him alone: if he shall hear thee, thou hast gained thy brother.
16 But if he will not hear thee, then take with thee one or two more, that in the mouth of two or three witnesses every word may be established.
17 And if he shall neglect to hear them, tell it unto the church: but if he neglect to hear the church, let him be unto thee as an heathen man and a publican.