“Is a division of practical theology concerned with persuading people of other faiths (or no faith) of the truth of the Gospel message, with an end to producing in them an awareness of, and sense of guilt for, their sins, a recognition of their need for God's forgiveness, repentance ( i.e. the disposition to turn away from their sin) and faith in Jesus Christ as Savior and Lord.” 
This theological technique encompasses more than the definition above can express. The primary idea is that of logical persuasion while engaging a person in their own culture, ideations or worldview. Taking into consideration who they are and bringing logical arguments to them in a manner that would persuade them out of their current worldview. This requires a personal touch – getting to know the person and their culture or worldview, like Paul did in Romans chapter 5. He knew the Romans had no knowledge of Biblical origins, so instead of just preaching Jesus crucified and risen, he took the Romans all the way back to the beginning in Genesis. 
Part of elenctics is bringing a person to the realization that they are a sinner in need of salvation. This will often elicit guilt in the individual or group as you logically share the reasons they need to repent and seek God’s forgiveness. Then the Gospel can be shared, and the person led by the Holy Spirit can accept Jesus Christ as Lord and Savior. They have to realize they are lost sinners before they can be saved.
Again, all of this must be received within the person or group’s worldview, ideology or culture. It must also be both demonstrated and proclaimed. It has been said, “I’ll just show myself as an example of how a Christian should live and that can lead people to Christ.” The person saying that understands that they must live a Christ-like life according to scripture, as much as humanly possible. Unfortunately, they can’t stop there. They must also proclaim the Gospel to the person or group. These things go hand-in-hand and cannot be separated when you encounter potential converts. You must not only show yourself worthy, but proclaim the Gospel. One aspect without the other is inadequate. This is not my opinion, but the truth from a careful study of scripture. Ephesians 4:1-3, Colossians 1:10, 1 Thessalonians 2:12-13, 2 Timothy 2:15, Romans 10:17, Ephesians 6:13-17, Colossians 3:17, 1 Thessalonians 2:13, Hebrews 4:12, Acts 1:8
The essence of Christian Elenctics, is to share the Gospel both in word and deed, in a personal manner that engages the other person in a way that is culturally acceptable to them, using logical persuasion and information from the Word of God.
 "Elenctics," Wikipedia, the Free Encyclopedia, last modified June 7, 2017, https://en.wikipedia.org/wiki/Elenctics.
 Aviles, "Christian Leaders Institute: Log in to the Site," Christian Leaders Institute, n.d. https://moodle.christianleadersinstitute.org/mod/url/view.php?id=30892.