First, we must pray for them. When we pray, we acknowledge that we rely on the Lord’s power. We must not be confident in our own brilliance (Philippians 3:3); it is the Holy Spirit who draws people to Jesus (John 16:7-11; 12:32).
Second, we must speak the truth in love, treating atheists with gentleness and respect (Ephesians 4:15; 1 Peter 3:15). When we witness to others, we are not trying to win debates; rather, we are trying to lead them to Christ.
Third, don’t try to prove God’s existence beyond all reasonable doubt. Though this can be done, the goal is often too lofty. Our goal should be more modest: argue that theism (belief in God) is more reasonable than atheism (the rejection of belief in God).
Discuss common aspects of human experience–aspects accepted by both atheists and theists. Then argue that theism is a more reasonable explanation than atheism. Both sides agree that the universe had a beginning. It seems more reasonable to conclude that something outside the universe (i.e., God) caused it to exist than to believe that the universe popped into existence totally out of nothing and without a cause.
Also, the design in the universe–including its living inhabitants–implies that the universe had an intelligent Designer. A single-celled animal contains enough genetic information to fill 20,000 volumes of an encyclopedia. It is not possible to produce that amount of information by chance. Again, theism offers a more reasonable explanation.
Both atheists and theists believe in human rights. Yet, in a universe without God, there are no human rights. If atheism is true, then people are mere molecules in motion and not deserving of rights. Either God created us in His image and gave us human rights, or we are the product of irrational processes and have no rights. Once again, theism offers a more plausible explanation than atheism.
Other aspects can be explored while dialoguing with atheists. These include the existence of universal moral laws, the continuing existence of the universe, the fact that human beings have knowledge, the existence of unchanging truths, the meaning of life, feelings of guilt, fear of death, and free will and human responsibility. Mere molecules in motion, combined with time and chance, cannot explain any of these factors.
Fourth, be willing to simply plant seed. Stay in touch with your atheist friends, love them and pray for them. Atheists will probably gain more respect for your views if you establish lifelong friendships with them.
Finally, remember that for an atheist to believe that God exists is only the beginning. They still need to be persuaded that Jesus is the Son of God, Who died on the cross for our sins and rose from the dead to conquer death for us. Unless atheists accept the true Jesus of the Bible as their personal Savior, they are still outside the Kingdom of God.