“For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek.” (Romans 1:16, ESV)
There are many reasons we don't grab opportunities to present the gospel when those opportunities present themselves. Fear of rejection, feeling inadequate, thinking "my conversion experience is nothing extraordinary" - all of these are excuses we make to shy away from presenting the gospel message to those we come in contact with on a daily basis.
It's good to remind ourselves the difference between God's role in evangelism and our role. If we try to take on God's role in this task, it's going to be incredibly frustrating. God makes "his light shine in our hearts to give us the light of the knowledge of the glory of God in the face of Christ" (2 Corinthians 4:6). He is the one who enables us to recognize that Jesus is God. By the power of His Spirit He changes hearts of stone to heart of flesh. He peels the blindness from our eyes so we can see His gracious goodness. Jesus Christ and He alone is the author and perfecter of salvation (Hebrews 12:2).
Our role in evangelism is to "herald" the message of the Gospel of the Good News. Our responsibility is to tell people the gospel and leave the Spirit of God to convict those who hear of its truth. We are called to be "servants for Jesus' sake (2 Corinthians 4:5). As "servants" we are "slaves" to the one who has called us, serving Him who saves. We are called, as the Apostle Paul, to present Christ and him crucified without any hint of self-promotion.
Our role in evangelism involves integrity, fidelity and humility.
Integrity in that we have a responsibility to be straightforward with people, genuine and sincere without using emotional manipulation.
Fidelity in that we do not distort the word of God (2 Corinthians 4:1-6). As slaves to the one who has called us, we have to tell the full message of the Gospel - the good with the bad. Preaching the full message of the Gospel means presenting hard truths that are sometimes difficult to hear, all the while, trusting in the Holy Spirit to draw people to Christ.
Humility in that "we do not preach ourselves, but Jesus Christ as Lord." We must decrease so He might increase (John 3:30).
We don't save anyone. Salvation is a work of our Triune God from beginning to end. Isn't it wonderfully amazing that God calls us to be a part of that as we go, present the message of the Gospel of Jesus Christ, sowing, planting, watering seeds (Isaiah 55:10-11; Matthew 13:18-23), all the while remembering God's role and ours in the extension of His Kingdom.