The four criteria of authenticity according to the textbook, The Cradle, The Cross, and The Crown are the criterion of Multiple Attestation, the Criterion of Palestinian Environment, the Criterion of Dissimilarity, and the Criterion of Coherence.
The Criterion of Multiple Attestation is simply whether or not the same event and saying occur from more than one source that do not rely one each other. Therefore, when an author write about Jesus, to be reliable it would also have to be found from another author who did not use the first author as a source for the material.
The Criterion of Palestinian Environment should be fairly self explanatory, where the material needs to make sense in the Palestinian environment. Therefore, if the phrase being used is not something that would make sense in Palestine during the time of Jesus, it would not be considered. The other side of this criteria is that material likely is authentic if the material would require someone with intimate knowledge of the locale or the language at the time. So when a phrase is used that may not make sense in modern vernacular (or vernacular from any other time period) but does make sense as a common phrase from Palestine at the time of Jesus, the material likely is authentic.
The Criterion of Dissimilarity is where material may not be so consistent with the theology of Judaism at the time, nor so consistent with the early members of the religion. This criterion is tricky because as N.T. Wright argues, “no historical person differs too radically from his immediate context. One would also expect significant continuity between the founder of a movement and his earliest followers. However, a truly distinctive leader will differ from others in his context in important ways, and his followers may prove incapable of fully imitating him.”
The Criterion of Coherence comes into usefulness when material does not fit the first three criteria discussed above, but the material is something that would likely by said by the subject (in this case Jesus). In short, just because material doesn’t fit into one of the first three categories, if it is something that, based on the rest of the material that has been shown to be authentic already, would likely be said by Jesus, the material is likely authentic.
In answering a skeptic of the gospels, I would start out by keeping things simple and allowing for a more detailed discussion later when more material could be answered, but to keep things quick I would tell the skeptic that the Bible as a whole is one of the most accurate documents in all of history. The New Testament being even more reliable than the Old just based on the manuscript evidence alone. It is the most documented book that we currently have and likely the exact words that are in the Bible are what was originally written.
Second, the feats that were accomplished could only have been accomplished in one person, and every other person in history has been disqualified. The miracles that happened are called miracles for a reason. They wouldn’t be hard to believe if they obeyed the normal laws of physics and life. The rest of the life of Jesus can be attested to in many ways, and although I can’t rattle off everything off the top of my head, if (s)he gives me the reasons why they don’t believe the gospels, I can find out more about any topic to give reasons.
But ultimately, I would challenge the skeptic by asking what is in their life that makes them not want to be accountable to a holy God who has come down to remove their sins and allow them to fellowship with Him? What is it that keeps them from humbling themselves and accepting what God has done for them?
 Kostenberger, Andreas and L Scott Kellum and Charles Quarles, The Cradle, The Cross, and The Crown: An Introduction to the New Testament (Nasheville: B&H Publishing) 152
 Kostenberger, Andreas and L Scott Kellum and Charles Quarles, The Cradle, The Cross, and The Crown: An Introduction to the New Testament (Nasheville: B&H Publishing) 151