The way I see it, the gospel and the kingdom of God are all about planting, watering, and faith. When it comes to us sharing the gospel our job is to plant and water seeds. It's God who makes things grow.
"What then is Apollos? And what is Paul? Servants through whom you believed, even as the Lord gave opportunity to each one. I planted, Apollos watered, but God was causing the growth. So then neither the one who plants nor the one who waters is anything, but God who causes the growth. Now he who plants and he who waters are one; but each will receive his own reward according to his own labor. For we are God’s fellow workers; you are God’s field, God’s building." (1 Corinthians 3:5-9)
It's the Holy Spirit that's doing the work of reaching the unbeliever, not us. We are simply the ones who share the gospel. In many cases the results may seem disappointing, but we should not be discouraged. God has not called us to convert people, but to share the gospel. No one expects a seed to produce a harvest the same day that seed is planted, so in the same way, we should not expect to see immediate fruit from our evangelizing.
We can only do our part which is to share the gospel and love the people as Christ loves us. We have no idea what God is doing in the lives of all the people we encounter and/or share the gospel with and we may never know. Someone we share the gospel with today may or may not come to Christ, but they may share what we have told them about Jesus with someone else in the future at which time the Holy Spirit convicts that person; a person we have never encountered or may never meet.
In addition to sharing the gospel we need to also remember as personal witnesses to Jesus Christ and the gospel, living our lives in a Christlike manor and treating others with a Christ-like attitude is of utmost importance. The simple acts of showing kindness, love, and compassion towards those who are lost may be all it takes to eventually lead them to the Truth. Living by example is at the foundation and perhaps one of the most crucial components of our personal witness to Christ to others. Most everyone in the unbelieving world has heard about Jesus, some many times over, but they may not have seen Him in action even once.
“For to this you were called, because Christ also suffered for us, leaving us an example, that you should follow His steps” (1 Peter 2:21)