The New Testament describes rapid growth of the church.  Some special individuals are highlighted, but the “regular” Christians seem to have done most of the one-on-one teaching:

Acts 8:4  Those who were scattered went everywhere preaching the word.

Romans 1:7  Your faith is spoken of throughout the whole world.

1 Thessalonians 1:8  From you the Word of the Lord has sounded forth, not only in Macedonia and Achaia but in every place.  Your faith toward God has gone out, so that we do not need to say anything.

The most extensive description of evangelism is in 2 Corinthians 4 – 5:

3:18  These chapters are addressed to all who are, “with unveiled face, beholding as in a mirror the glory of the Lord.”

4:1  “As we have received mercy, we do not lose heart.”  Focus on the mercy I have received (God was motivated by compassion to fix my flaws), not numerical success, as the motivation for evangelism.  This allows us to endure the fact that 99% of the people we try to reach do not care about God.  In 4:16, the fact that my physical body is falling apart is overshadowed by the fact that my eternal body is gaining daily.  (cf. 4:17 – 5:6)

4:2  “We have renounced the hidden things of shame, not walking in craftiness nor handling the Word of God deceitfully, but by manifestation of the truth commending ourselves to every man’s conscience.”  Clever approaches are not desirable.  Presenting ourselves as honorable people will bring hearers.  What we need to present are the facts, not emotional appeals.  In 4:5, “we do not preach ourselves.”  In 4:6, the proper evangelistic method is to let God’s character shine from you, which is very similar to the thought in 3:18.

4:3  “Even if our gospel is veiled, it is veiled to those who are perishing.”  If we are honorable and factual, we can be certain that the low response rate is not due to us.

4:7  The proper evangelistic method is to be doing things that outsiders plainly can see are beyond your ability.  Paul gives examples from his life in 4:8 – 12.  In 5:7, doing the impossible is called faith, in contrast to sight.

4:13  Your examples of doing the impossible and displaying godly character must be accompanied by words coming out of your mouth.  It’s a package deal.

5:11  Another motivation for evangelism is our fear for the destination of people we know.  Therefore, we speak (persuade).  In 4:16, evangelism is made possible by seeing the spirits of others.

5:14  The love of Christ compels us.

5:18  We have a ministry of reconciliation, not of judgment.  Those who care about being reconciled to God will listen.

5:20  We are ambassadors: courteous, diplomatic, carefully spoken.

Note the lack of methodology.  Speaking is necessary, although the type of speaking is open.  Personal conversation is probably more effective than impersonal preaching and teaching.  Visible and obviously impossible behavior is necessary.  The rest is open to personal preference.