The word, "apologetics," comes from the Greek word, "apologia," pronounced "ap-ol-og-ee’-ah." It means "a verbal defense." It is used eight times in the New Testament: Acts 22:1, 25:16, 1 Cor. 9:3, 2 Cor. 10:5-6, Phil. 1:7, 2 Tim. 4:16, and 1 Pet. 3:15. But it is the last verse that is most commonly associated with Christian apologetics.
1 Pet. 3:15, "...but sanctify Christ as Lord in your hearts, always being ready to make a defense to everyone who asks you to give an account for the hope that is in you, yet with gentleness and reverence."
"Apologetics is the work of convincing people to change their views."
Therefore, Christian apologetics is that branch of Christianity that deals with answering any and all critics who oppose or question the revelation of God in Christ and the Bible. It can include studying such subjects as Biblical manuscript transmission, philosophy, biology, mathematics, evolution, and logic. But it can also consist of simply giving an answer to a question about Jesus or a Bible passage. The latter case is by far the most common, and you don’t have to read a ton of books to do that.
Apologetics can be defensive and offensive. Phil. 1:7 gives us instruction on the defensive side, "For it is only right for me to feel this way about you all, because I have you in my heart, since both in my imprisonment and in the defense and confirmation of the gospel, you all are partakers of grace with me." 2 Cor. 10:5 gives us instruction on the offensive side: "We are destroying speculations and every lofty thing raised up against the knowledge of God, and we are taking every thought captive to the obedience of Christ." The apologist can and should defend his reasons for believing (1 Pet. 3:15). But he can also go on the attack. He can seek out those who oppose Christianity (2 Cor. 10:5). Of course, he should be prepared to do this beforehand, and all apologetics is to be done with gentleness.
Apologetics is the work of convincing people to change their views. In this, it is similar to preaching because its goal is ultimately the defense and presentation of the validity and necessity of the gospel. It is an attempt to persuade the listener to change his beliefs and life to conform to Biblical truth and to come to a saving relationship in Christ.
Basically apologetics can be evidential (often called "classical") or presuppositional. Evidential apologetics deals with the evidence for Christianity: Jesus’ resurrection, the Biblical manuscripts, fulfilled prophecy, miracles, etc. Presuppositional apologetics deals with the presuppositions of those who oppose Christianity because presuppositions affect how a person views evidence and reason.
Some areas of debate within Christian apologetics deal with the use of evidence, reason, philosophy, etc. Should the apologist use only those criteria acceptable to unbelievers? Are we allowed to use the Bible as a defense of our position, or must we prove Christianity without it? Is reason alone sufficient to prove God's existence or Christianity’s truth? How much should reason and evidence be used in light of the Scriptures' teaching that it is God who opens the mind to understand? What part does prayer, using the Bible, and the sinful nature of the unbeliever play in witnessing? How do these factors interrelate to bring an unbeliever to faith? The questions are easy. The answers are not.
Jesus chose one highly-educated religious person as an apostle. That was Paul. The rest were fishermen, a tax collector, a doctor, etc. They were normal people of the day who were available and willing to be used by the Lord. They were filled with the Spirit of God, and they were used as vessels of God. God uses all things for His glory. So, we do apologetics by faith.
The Lord has called every Christian to be ready to make a defense of his faith. That means you are called to give reasonable answers to questions regarding Christianity. Now, this does not mean that you must have a Ph.D. or that you have to go to seminary. However, it does mean that you should be willing to at least give an answer for your beliefs. If you find you cannot, then prayerfully take it to God and start studying.
What do you study?
You could pray and ask the Lord to teach you what He wants you to know. Ask Him to give you a burden for something to learn. It doesn’t matter what it is. Just ask. Whatever you become interested in is what you should learn about because it is probably something God wants you to know for later use. It is like having tools in a tool shed. The more you have, the more you can accomplish.
Another way to find out what God wants you to study is through circumstances. Let’s say that a Jehovah’s Witness comes to your door and debates the deity of Christ with you and you find that you don’t know how to defend it Biblically. In that case, you know you need to study Biblical verses that teach Jesus is God in flesh. Or maybe a coworker asks you how you know the Bible is true? If you don’t have an answer, pray, and start researching. Go to a Christian bookstore and get some books on the subject. Talk to your pastor. You’ll learn.
Sometimes God will make a verse or subject in the Bible "come alive" to you, and it might strike you as odd or interesting. You could get a commentary and read up on it. You could ask others about it. In so doing, you are preparing yourself through learning to be ready to answer questions and point people to the truth. You'd be surprised how many details God can use to help you in your witness even through those apparently odd times when verses suddenly "come alive."