C. H. Spurgeon defined the gospel this way: Jesus died for me. That is our essential message. It is Jesus Christ and Him crucified.
I think we overcomplicate this thing we call evangelism way too much. I am not suggesting that we go out and start telling others about Christ without any understanding of what the Bible teaches. There is a place for apologetics, the defense of the faith. There is a place for building a bridge with those we are speaking to, and there is a place for other evangelism techniques that we might employ. But the bottom line we are to reach, the primary message we are to proclaim, is the message of Jesus Christ and Him crucified.
And it is my belief that as you proclaim this message, God can use you to win others to Christ. The apostle Paul wrote, "For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God" (1 Corinthians 1:18), and "I am not ashamed of the gospel of Christ, for it is the power of God to salvation for everyone who believes, for the Jew first and also for the Greek" (Romans 1:16).
I have been proclaiming the gospel message for 35 years now, and I am still amazed at its power. I have heard the stories of people whom you would never expect to believe in Jesus. I have been astonished at the way God reached them and transformed them. It is the power of the gospel.
There is power in the simple story of the life, death, and resurrection of Jesus. Don't complicate it. Don't add to it. Don't take away from it. Don't apologize for it. Just proclaim it, and watch what God will do.