These are my personal Bible study notes on the topic of personal evangelism.

Matthew 5:13-16 You are the salt, the light of the world. Don't hide your light under a basket.
Matthew 9:35-38; Luke 10:2 Labourers for the harvest.
Matthew 10:27
1 Corinthians 9:20-23 To the Jews I became a Jew, to those without law, as without law... if by any means I might save some.
Colossians 4:5-6 Walk in wisdom towards those who are outside, redeeming the time. Speech be with grace, seasoned with salt, to know how to answer each one.
1 Peter 3:15 Always ready to give a defense for the hope that is in us.

Caveats

Proverbs 9:7-8 Don't try to correct/teach a scoffer.
Proverbs 28:28 When the wicked arise, men hide themselves, But when they perish, the righteous increase.
Matthew 7:6 Don't throw your pearls before swine.
John 6:44 No-one can come to Jesus unless the Father draws them in. We can't convert anyone by our own strength.
1 Corinthians 1:18-29 The message is foolishness to those whom God is not calling.

Other objections

• "Don't proselytise. It's not our business to proselytise to people who are not interested in hearing it." Yet, Paul essentially proselytised to Jews about Jesus, in their synagogues, on the Sabbath day. Eg Acts 17:1-4.
• "If someone asks me, then I'll answer their questions. But I'll never tell someone what I believe unless they ask."
• "The work of preaching the gospel to the world is done by the church, not by individuals."
• "There's no sense in sticking your neck out in a wicked world." (Proverbs 28:28)

Study How to Answer

Proverbs 15:28 Study how to answer.
Matthew 10:16-20 Be wise as serpents, harmless as doves. Counter-point: don't worry how to answer, when brought before kings, but rely on the Holy Spirit. Luke 21:14 puts it more strongly, saying not even to plan how to answer.
Colossians 4:5-6 Walk in wisdom towards those who are outside, redeeming the time. Speech be with grace, seasoned with salt, to know how to answer each one.
1 Peter 3:15 Always ready to give a defense for the hope that is in us.

Personal Example

Matthew 5:13-16 You are the salt, the light of the world. Don't hide your light under a basket. People may see your good works and glorify God.
John 13:34-35 Love one another. By this people will know you're disciples of Jesus.
1 Peter 2:11-17 Live with good conduct and good works as an example to the Gentiles.
1 Peter 3:1-2 Believing women may win over their unbelieving spouse by their example of good conduct.

Boldness

Deuteronomy 31:6; Joshua 1:9 Encouragement to Joshua.
Psalm 27:1; 56:3-4; 118:5-6 Trust in God.
Proverbs 28:1
Acts 4:13,29-31; 5:29-32,41-42; 13:46; 19:8; 28:31
Ephesians 6:19-20
Philippians 1:12-20
1 Thessalonians 2:2
2 Timothy 1:6-7
Hebrews 13:5-6 which quotes Psalm 118:6.
1 John 2:28

Don't Be Ashamed of Jesus and the Gospel

Matthew 10:32-33; Mark 8:38; Luke 9:26; 12:8-9
Romans 1:16-17
2 Timothy 1:8-12

Examples

Acts 2 Peter on first New Covenant Pentecost. He preached the resurrection of Jesus.
Acts 3:11-26 Peter preached the unjust suffering and death of Christ, and His true identity.
Acts 4:5-12,19-20 Peter and John testified to the Sanhedrin about Jesus and His death and resurrection.
Acts 5:27-32,41-42 Again before the high priest.
Acts 7 Stephen's speech, for which he was stoned. He criticised them for resisting God just like their Israelite ancestors.
Acts 8:26-40 Philip preached Jesus to the Ethiopian eunuch. God provided a perfect set-up for him.
Acts 9:19-22 Paul was converted by Jesus. He started preaching that Christ is the Son of God, the Messiah.
Acts 10:34-48 Under miraculous circumstances, Peter comes to Gentile Cornelius and his family. He preaches Jesus and salvation of Gentiles.
Acts 13:13-43 Paul at the synagogue at Antioch in Pisidia. They preached the death and resurrection of Jesus, and justification through Him that couldn't be done through the law.
Acts 14:8-20 Paul and Barnabas at Lystra. They were called Zeus and Hermes. No preaching about Jesus in this situation. More basic preaching about the one true God of heaven and earth.
Acts 17:1-4 Preaching Christ in the synagogue at Thessalonica.
Acts 17:16-34 Preaching at the Areopagus in Athens. He concluded with proclaiming the resurrection of Jesus, but built up to it first by preaching the one true God.
Acts 18:4-5 Paul preached Jesus is the Messiah, in the synagogues of Corinth on the Sabbaths.
Acts 19:1-10 Paul preached the "things of the kingdom of God" in the synagogue of Ephesus, and later in the school of Tyrannus, the "word of the Lord Jesus", to Jews and Greeks.
Acts 22:1-21 Paul gave a defence in Jerusalem, telling of his calling by Jesus and his assignment to preach to the Gentiles. That last bit enraged his audience.
Acts 24:1-21 Paul gave his defence before Felix, preaching the resurrection.
Acts 26:1-23 Paul gave his defence to Agrippa, again telling of his calling by Jesus, previous persecution of believers, calling of Gentiles, suffering, death and resurrection of Jesus.
Acts 26:24-28 Agrippa told Paul, "You almost persuade me to become a Christian."
Acts 28:17-31 Paul's preaching in Rome. He persuaded them concerning Jesus, from Moses and the prophets.
1 Corinthians 1:17-25; 2:1-8 Paul's description of his preaching about Jesus, the power of God and not clever human reasoning.
Philippians 1:12-14 Even while Paul was in chains, he saw how God was making it an opportunity to preach the gospel to those around him.