Here's an excellent revision (or update) and presentation of Van Til's presuppositional method of apologetics: Covenantal Apologetics: Principles and Practice in Defense of Our Faith, by Scott Oliphint (Crossway, 2013). Here are some initial hightlights...
"...in your hearts honor Christ the Lord as holy, always being prepared to make a defense to anyone who asks you for a reason for the hope that is in you; yet do it with gentleness and respect..." (1 Peter 3:15 ESV)
"...unless one begins from God’s authority, revealed in the world and in the Scriptures, then we will always have an inadequate foundation for our views and our lives."
"Christian apologetics is the application of biblical truth to unbelief."
"...if one is to be adequately prepared to give an answer for one’s Christian faith, the lordship of Christ must be a solid and unwavering commitment of one’s heart."
"The point for the Christian, however, and the point to stand on in a covenantal apologetic, is that Christ’s lordship—which includes not only that he now reigns, but also that he has spoken and that all owe him allegiance—is true for anyone and everyone."
"The weapons of our warfare are divine weapons, and they have their focus in the sword of the Spirit (Eph. 6:17)."
"...the basic principle is this: a covenantal apologetic must proceed on the basis of reality and not on the basis of illusion. We must proceed according to what Christ, who is the Lord, has told us, not according to what our opponents have decided is 'appropriate' for a defense of Christianity."
"So in knowing a particular thing, man knows God who reveals himself in and through that thing (including man himself)... True self-knowledge depends on God-knowledge (and vice versa)."
"...since the fall, given the above, we became, in the truest sense of the word, irrational. That is, we sinfully and deceptively convince ourselves that what is actually true about the world is not true. We create a world of our own making, where we are all gods. What we now seek to do and how we seek to live and think are set in polar opposition to the world as it actually is... we seek the utterly impossible and unobtainable; we seek autonomy."
"This is what a covenantal apologetic seeks to do. It seeks to take the truth of Scripture as the proper diagnosis of the unbelieving condition and challenge the unbeliever to make sense of the world he has made."
"...covenantal apologetic is transcendental. A transcendental approach looks for the (so-called) preconditions for knowledge and life. It does not simply assume that knowledge is the same for believer and unbeliever alike. Instead, this approach asks questions about the basic foundations of an unbelieving position."
"The very reason there is a debate between us is that our respective authorities are in conflict."