This book is more about the method of doing apologetics, rather than arguments for Christianity. I didn't really know there were sub-schools in how to present a rational argument, but it turns out theologians need something to disagree with.
William Lane Craig, one of the more famous Evangelical apologists, put forward The Classical Method. This method sets out to first prove that "God" exists, moving someone to theism. Once that is established they then set out to prove Christianity. The reasoning is that for people to believe in say Jesus's miracles, or that God has revealed Himself in the Bible, first someone needs to think miracles or God being able to speak are plausible, ie. God exists in the first place. This is known as a "two-step method".
On The Evidential Method was Gary R Habermas, who I think is one of the best arguers for the resurrection of Jesus. Habermas sees the historic argument for Jesus' resurrection so powerful that you don't first have to establish that God exists. If you look at the evidence and see that Jesus rose from the dead, from that you would then have to concede that God exists. Unlike trying to argue first for theism, they think, just cut to the chase and argue for Christianity and you get theism thrown in. This is known as a "one-step method", I think I kinda used this method (without knowing it) in this post a few years back, (although the question presupposed the Bible already).
Paul D Feinberg was on The Cumulative Case Method side of things. This method sees that the classical proofs for God are good (to some extent), and so is the historical evidence for Jesus (to some extent), but so is a bunch of other things like our sense of morality and justice and other social things. The idea here is that, there isn't one (or two) knock down arguments for Christianity, but more each argument is just one point of evidence. These arguments don't need to build off each other, they may just make a completely separate point. It reminded me a little bit of something G. K. Chesterton said in his book Orthodoxy (forgive me for the long quote. I just really like Chesterton):
If I am asked, as a purely intellectual question, why I believe in Christianity, I can only answer, “For the same reason that an intelligent agnostic disbelieves in Christianity.” I believe in it quite rationally upon the evidence But the evidence in my case, as in that of the intelligent agnostic, is not really in this or that alleged demonstration; it is in an enormous accumulation of small but unanimous facts. The secularist is not to be blamed because his objections to Christianity are miscellaneous and even scrappy; it is precisely such scrappy evidence that does convince the mind. I mean that a man may well be less convinced of a philosophy from four books, than from one book, one battle, one landscape, and one old friend. The very fact that the things are of different kinds increases the importance of the fact that they all point to one conclusion. Now, the non-Christianity of the average educated man to-day is almost always, to do him justice, made up of these loose but living experiences. I can only say that my evidences for Christianity are of the same vivid but varied kind as his evidences against it. For when I look at these various anti-Christian truths, I simply discover that none of them are true. [you will have to read on to see why he thinks so]
My man, John M Frame was on The Prepositional Method team. In this method, we need to work out that everyone has an "truth source" that they appeal to and use for the bases of everything else. This could be experience, or their own reasoning/mind, or their sense or what a Holy Book says. What we use as our "truth source" can only be defended by appealing to it. My reasoning is true because my reason tells me it is. My experiences are true because that is what I experience. The Bible is true because it says that it is. This means everyone, Christians included, defend their case in a circular argument, so the goal in presenting Christianity is not for its logical rigor, but instead to just be persuasive in light of the Christian world-view and present arguments from it, not to argue to it. This is more philosophic, but the Christian world-view should be presented to show that everything - thought, logic, love - all come from the Biblical God and not from any other "truth source".
Lastly, Kelly James Clark put forward The Reformed Epistemological Method. This method seems to be a new introduction to the apologetic sub-category. This one holds that people don't necessarily live out consistent world-views, so the emphasis we put on evidence or arguments for God are lacking. Instead, if apologetics is more about bringing someone to faith than arguing for it, we should see how people actually come to faith and remember that God is not some natural law, but a person. This means religious experiences and consideration of these should be more emphasised.
This was a counterpoints book, which meant that after each chapter, the four other authors got to critique it. Then, at the end, each author again got to respond to comments they got at the end of their chapters. Since this was a "five views of X" book, it mean that it got quite long. Next time I am reading a "three views of X" book.
From their comments there was much agreement. Even others calling people as belonging to their own camp. I must say that I think Frame, the reason why I started reading this book, got a bit pantsed. His admission to having a circular argument does not hold up well with people who argue logic. Sometimes I would read a chapter and think "yeah X sounds good" and then read a counter point and then think "oh yeah, they are wrong on X", this is because all of the authors are quite good at arguing (I mean what else is apologetics :P).
One of the main issues with each of the methods really comes down to how much you think sin has affected someone's reasoning skills. This is called the noetic effect of sin. How do you weigh up the noetic effect with the common grace that God has given to everyone? Do reason and logic help, or are people incapable of theological reasoning because of sin, and is it all really the work of the Holy Spirit anyway? My answer is "yes". Yes conversions are all the work of the Holy Spirit. Yes, unbelievers don't and can't think about theological issues with any real clarity from God. Yes all people have common grace of logic and reasoning. So I think the Holy Spirit can use ordinary means, like logic and reasoning, along with certain experiences, or friends in their life to bring about conversion. I think God can use any method in this book (and more, less logically sounding ones) to bring about salvation. After all, God saved me.
If you are interested in this issue, read the following links and if you are still interested, then get this book.