The points on this page may shake the faith of the Atheist in the precepts of Atheism, but the most important thing is that you share the Good News (Gospel). This is simple. All these other things may help, but it is the proclamation of the Gospel that transforms minds. See Give Them the Gospel.
Satan has invested considerable effort in spreading lies. Those who have been victims of those lies are held captive by them. Often, until the lie is dealt with, the person cannot be set free. These people scoff because they are slaves of Satan and Satan keeps them in slavery with lies.
A large portion of the population has been brainwashed into ungodly thinking. For this reason, the gospel is meaningless to them. If there is no creator God, then there is really no right or wrong. What would then be the basis for saying that someone had sinned? Who then needs atonement?
The reason that people become confused and don't know the difference between truth and error is because they don't want to do God's will. You can answer all the questions of a person who doesn't want to do God's will and they will not be able to accept it. "To try to explain truth to him who loves it not is but to give him more plentiful material for misinterpretation." George Macdonald "How frequently it is brought to our attention that nothing good can be done if the will is wrong! Reason alone fails to justify itself." Richard M. Weaver "If we are not prepared to buy the truth at the cost of our own humbling we shall not receive it"
Jesus said, "If you really want to obey God, you will know if what I teach comes from God or from me." Anyone who really wants to obey God will receive truth and reject error. This is true whether the person has been born again or not. Some people are born again and never grow up at all because they don't want to obey God and they cannot tell the difference between the truth and a lie. They read the Scripture and cannot hear God's voice. God cannot reveal anything to them since they refuse to cooperate with the Holy Spirit.
Every Christian who is a Christian should have the answers to several questions regarding Evolution and the Age of the Earth. Remember that, though there is a volume of material evidence for God, only a small part of the evidence that we have is material. There is no scientific fact from any branch of science that refutes the God of the Bible or the Bible. This is true. However, you must keep in mind the reason that you believe is not because you can answer all the questions that come your way and that you can show that every way other than the way of Christ is lacking. If you are a Christian, then Christ has and is revealing Himself to you. You know that the Bible is the Word of God because the Almighty Creator God has shown you that this is the case. Build on Rock and not on sand. Christ is the Rock. Have a real relationship with Him. Don't lean on your own understanding.
We are not dogmatically claiming to know that the Earth is 6,000 years old. We know that God created the Heavens and the Earth in six days and we know the number of generations between Adam and Christ. That's about it. Even though a plain reading of Scripture seems to indicate a young Earth; even though there is zero observed evidence and only circular reasoning and speculations that support old Earth stories, we can't even deny the possibility that God could have done something that Scripture doesn't hint at and that has left no scientific evidence. It is possible. It just is not worth the time to think about it.