According to Bill Bright, only 2% of Christians share their faith. One of the reasons for this is that they don't feel equipped.
Most people are afraid to share their faith anyway, with a few obnoxious atheists mocking Christianity as "un-scientific" and "crutch for weak minded people". I find it quite the opposite, with the theory of evolution being un-scientific (life coming from non-life and violations of various scientific laws) and more of a crutch for those who want to think that they will not be held accountable for their actions. But that doesn't even matter and is an entirely separate topic for anyone interested in such things.
We don't even need to go there. Instead, we can go directly to the conscience, (con means ;with', and science is 'knowledge'), and when someone sins against God, they do it 'with knowledge'. The conscience itself is an ally in witnessing.
There is a simple Biblical principle that has been largely forgotten in the modern Church in the last couple of hundred years. Rather than a man-made "sinners prayer" or some sort of "altar call", made famous by Charles Finney in the 1800's, we should go back to the Bible, the authority of God's Word and witness the way that our Lord and Savior, Jesus Christ did it.
Check out His example in speaking with the woman at the well (John 4:4-29). First, He spoke to her about natural things, getting a drink of water in this instance. Then he moved to the spiritual realm, telling her of the living water. Being convicted of her sins, she went back into town to tell others about Him.
When the rich young ruler came up and called Him good, he was right. But Jesus reproved the man, for he did not understand what 'good' truly meant. Only God is good. And when Jesus went through some of the Ten Commandments, the young ruler claimed that he had kept them (1 John 1:8). Then He asked the man to give up his riches and put God first in his life (the First Commandment) and the young ruler walked away. Jesus did not run after him, telling him of a wonderful plan for his life and how God loved him so much, He let him go (Luke 18:18-27).
The Bible tells us that the proclamation of the Gospel is always Law to the proud, Grace to the humble (Prov 3:34, 1 Pet 5:5, James 4:6), and Jesus did not deviate from this. I would challenge you to show me a passage where He did not follow it, keeping in mind that when He didn't go through the Law first, it was because the person was already humbled and knew of his need.
How would we know if someone is humble, knowing their need? It's simple, just ask them. "Would you consider yourself to be a good person?" Prov 20:6 tells you what they will say, "Most men, everyone will proclaim his own goodness...." yet the Bible tells us over and over again that there are none found good, not one (Psalm 53:3, Rom 3:23, Is 64:6).
Ask someone how they think one gets into heaven and you'll find the most common answer is by "being good." If that is true, then we earn our way into heaven, there was no need for Jesus Christ to die on the cross and the Gospel makes no sense. This would leave us with nothing but blind faith and no understanding. We wonder why "prosperity preaching" is so popular, and universalism is gaining ground in the modern churches, and terms like "carnal Christianity" abound. And then we wonder why atheists mock it.
What the Bible actually teaches is that there are none found good when we're held to God's moral standard, that every one of us deserves to spend eternity in hell for breaking His commandments, but that He actually created a plan of redemption for us. The fine had to be paid, and God came down in Jesus Christ, lived a perfect, sinless life, then laid down that life as a sacrifice to pay the penalty that we deserve, for the wages of sin is death. But death couldn't hold Him, and on the third day, He rose again, defeating death forever.
Now, all that we must do is put our faith and trust in Him, and when we do that, we will also repent of our sins, turning away from them, hating those sins that we once loved because we can see what it cost, and that God so graciously and lovingly paid that fine for us. We couldn't possibly continue to willfully live in a lifestyle of sin if we even begin to comprehend that (Heb 10:26-29).
If we will simply repent and trust in Him alone, we will be saved apart from works, yet we will do good works out of gratitude for the new life we have been given, released from condemnation and slavery to our own sinful nature.
To God be the glory, proclaim His name!