- But sanctify the Lord God in your hearts: and be ready always to give an answer to every man that asketh you a reason of the hope that is in you with meekness and fear: Having a good conscience; that, whereas they speak evil of you, as of evildoers, they may be ashamed that falsely accuse your good conversation in Christ. (1 Peter 3:15-16) (KJV).
To do apologetics is to defend one's faith. Therefore, the study of apologetics is the study of how to defend one's faith. There are many different ways to approach apologetics, most of which are outlined below.
"The goal of apologetics is to persuasively answer honest objections that keep people from faith in Jesus Christ." 
"The classical method is an approach that begins by employing natural theology to establish theism as the correct worldview. After God's existence has thus been shown, the classical method moves to a presentation of the historical evidences for the deity of Christ, the trustworthiness of the Scripture, et cetera, to show that Christianity is the best version of theism, as opposed to, say, Judaism or Islam. This school is called the classical method because it is assumed that this is the method used by the most prominent apologists of earlier centuries."  Contemporary apologists who may be classified at classical apologists include William Lane Craig, R. C. Sproul, Norman Geisler, Stephen T. Davis, and Richard Swinburne.
"The evidential method has much in common with the classical method except in solving the issue concerning the value of miracles as evidence. Evidentialism as a apologetic method may be characterized as the one-step approach. Miracles do not presuppose God's existence (as most contemporary classical apologists assert) but can serve as one sort of evidence for God. This method is fairly eclectic in its use of various positive evidences and negative critiques, utilizing both philosophical and historical arguments. Yet it tends to focus chiefly on the legitimacy of accumulating various historical and other inductive arguments for the truth of Christianity." 
"The term cumulative case is used by apologists in ways different than we are using it in this context, but Basil Mitchell, an early proponent of this view, gave this method that name, and so will wil use it here. The careful reader will no doubt note that this method belongs to the same broad family of methods as does the evidential (and perhaps classical) method. However, it will also be apparent that as an argumentative strategy, the cumulative case method has something distinctive to offer. Indeed, this approach to apologetics arose because of the dissatisfaction that some philosophers had with these other evidential-type methods (i.e., the first two of the Big Four)." 
"Due to the noetic effects of sin, presuppositionalists usually hold that there is not enough common ground between believers and unbelievers that would allow followers of the prior three methods to accomplish their goals. The apologist must simply presuppose the truth of Christianity as the proper starting point in apologetics. Here the Christian revelation in the Scriptures is the framework through which all experience is interpreted and all truth is known. Various evidences and arguments can be advanced for the truth of Christianity, but these at least implicitly presuppose premises that can be true only if Christianity is true. Presuppositionalist attempt, then, to argue transcendentally. That is, they argue that all meaning and thought - indeed, every fact - logically presupposes the God of the Scriptures." 
See main page on presuppositional apologetics.
"Since the Enlightenment, Clark says, there has been a demand to expose all of our beliefs to the searching criticism of reason. (...). We are told that if a belief is unsupported by evidence of some kind, it is irrational to believe it. Reformed epistemology challenges this evidentialist epistemological assumption. Those who advocate this view hold that it is perfectly reasonable for a person to believe many things without evidence. Most strikingly, they argue that belief in God does not require the support of evidence or argument in order for it to be rational. The Reformed epistemology apologist will not necessarily eschew making positive arguments in defense of Christianity, but will argue that such arguments are not necessary for rational faith. If Calvin is right that human beings are born with an innate sensus divinitatis (sense of the divine), then people may rightly and rationallly come to have a belief in God immediately without the aid of evidence."