There are different ways that this can be done, However, one must realize that if one to whom a Christia is witnessing to has a bias presupposition, no arguement known will convince him or her, however, Adam's rebellion brought sin into the world but it did not make mankind so depraved that he could not respond to God's offer of redemption if he chooses to.
Understand that The foundation to understanding God’s common grace is our nature. God made humans in His likeness and image (Gen. 1:26) which essentially means He has given us spirit, soul, moral conscience and a mind to reason. With this in mind, let’s examine Rom. 1:20 which says, "For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse." God has made an incredibly beautiful and complex creation which could only come from a Designer and only men choosing to suppress that truth in unrighteousness (Rom. 1:18) prevents them from acknowledging the Designer behind it. Unbelievers both acknowledge the amazing complexity of creation and experience the beauty of creation, yet they choose to turn to preposterous, illogical fables Like Evolution instead of turn to the Creator Himself. If they did not have the ability to acknowledge or experience the complexity and beauty of creation, then it could be soundly argued that they were so depraved that God would have to do a special irresistible drawing to Himself. The scripture, however, plainly says that man is "without excuse" because he willingly "suppress[es] the truth". The only way men could be "without excuse" is if they have the ABILITY to respond to this common grace, which they clearly do, yet choose instead to suppress the truth.
Now with that being said, Ways to witness non-believers can come with a form of Apologetics, Several types are used, like Tools on a Tool belt of a Construction worker, Apolgetic tools can be used as well depending upon the demenoir of the one to whom you are witnessing to,
Classical Apologetics is that style of Christian defense that stresses rational arguments for the existence of God and uses evidence to substantiate biblical claims and miracles. It is quite similar to evidential apologetics and appeals to human reason and evidence. Early Classical Apologists include Augustine, Anselm, and Thomas Aquinas. Contemporary classical apologists are Norman Geisler, William Craig, J. P. Moreland, and R.C. Sproul.
Evidential Apologetics is that style of Christian defense that stresses the miracles found in the Bible particularly Christ's resurrection as an evidence for the existence of God and the validity of Christ and His words. It also uses historical evidences to support the veracity of the biblical account(s). In this, it is very similar to Classical Apologetics, which stresses reason in its approach to evidences. Basically, evidential apologetics stresses evidence such as miracles, fulfilled prophecies, etc., and uses reason to support them.
Presuppositional Apologetics which is what I use the most, this form of Christian apologetics deals with presuppositions.1 A Christian presuppositionalist presupposes God's existence and argues from that perspective to show the validity of Christian theism.2 This position also presupposes the truth of the Christian Scriptures and relies on the validity and power of the gospel to change lives (Rom. 1:16). From the scriptures, we see that the unbeliever is sinful in his mind (Rom. 1:18-32) and unable to understand spiritual things (1 Cor. 2:14). This means that no matter how convincing the evidence or good the logic, an unbeliever cannot come to the faith because his fallen nature will distort how he perceives the truth. The only thing that can ultimately change him is regeneration. To this end, the presuppositionalist seeks to change a person's presuppositions to be in conformity with biblical revelation.
I have found that a person's presuppositions are extremely important when discussing God and the validity of Christianity. I always ask diagnostic questions to find out where a person is philosophically and presuppositionally, so I might better discuss Christianity. This is a very important point to focus on because one's presuppositions will govern how one interprets facts.
Presuppositional apologetics differs from Classical apologetics "in that presuppositional apologetics rejects the validity of traditional proofs for the existence of God."3 A pure presuppositionalist tackles the worldview of a person and seeks to change the very foundation of how a person perceives facts.
Adherents to this position have been Cornelius Van Til, Abraham Kuyper, Greg Bahnsen, John Frame, etc.
Following are some things I have found that are very helpful in developing apologetic skills. I am not saying that these are definitive or exhaustive in scope. Rather, these are simply the things that I have found that have helped me. I hope they help you.
Remember, there is no method for apologetics that works in all situations. There can be no outline approach that, if followed, will always lead a person to understanding and accepting the truth. That is why apologetics is a combination of what you know and are. It is a fluid expression that must adapt to the obstacles in its course.
Apologetic skill is directly related to your experience and knowledge. You gain knowledge by experiencing a situation where you defend the truth. This is "doing" apologetics. It is through this doing that you polish what you know, discover your areas of weakness, and plan ways to improve your abilities. You need to learn as much as you can through study, practice what you learn in real situations, think of ways to apply what you know, mess up, and keep going. All of this is what apologetics is and is how you get better. So, is there one single rule that will help you develop skill in apologetics? Yes, there is. Go for it! You will have success and failures.
Here are some Guidelines, Pray
It is the Lord who opens the heart and mind--not you (Acts 16:14). Ask God for guidance (John 14:14). Ask for blessing in your understanding (James 1:5) and your speech (Col. 4:6). Ask the Lord to also open their understanding to God's word (Luke 24:45).
Few things are as powerful when defending the faith as being able to cite chapter and verse of a particular verse (Psalm 119:11; 2 Tim. 3:16).
Memorize the locations of information
. . . whether it be in cult material, secular material, or any other source you've got. It is extremely valuable to know material in different disciplines. Of course, you cannot know everything, but you can memorize a few pertinent facts about Mormonism or evolution or philosophy or the Bible or whatever else may be needed. You will learn what you need as you witness.
Listen to what is being said to you
. . . and respond to what is said. It is by listening that you will then know what to say. Listen for errors in logic. Listen for motives, for hurts, for intent. Listen.
This is just common courtesy. You need to earn the right to speak. Just because you have an answer doesn’t mean it must be heard right away. When interruptions become the norm, learning is thrown out the window.
Don’t be afraid to make mistakes
One of the best ways to improve is to discover your weaknesses. The best way to discover your weaknesses is when mistakes uncover them for you.
Study what you discover you don’t know
If you don’t know something, then study it. Get books and read. Write down what you learn.
Don’t be afraid to take a chance
This takes real faith. All you have to do is be available, speak up, and take a chance in defending the Christian faith. You’ll be surprised at how well you do. And when you mess up, don’t worry--review guideline #6.
Perhaps the best place to do apologetics is in your head. Think of a situation, a scenario that you need to have an answer for and develop an answer. Practice in your mind. Try to corner yourself and then get out of it.
Read books that deal with what you need to know
The knowledge of others is invaluable. Isaac Newton said, "If I have reached the stars, it is because I have stood on the shoulders of giants." In other words, he learned from others.
Basically, the guidelines are common sense. All you have to do is try--don’t worry about failure, keep going, pray, and trust God. It works.