Since nearly all New Testament manuscripts lack a specific date on their pages or are written as codices, preventing termina dating, historians must rely on paleography to approximate the date of composition.
Paleography is, in essence, a method of determining a manuscript's date of composition through handwriting comparison. On the surface, such a technique may seem more art than science and very subjective, but when one delves into the nuances of the discipline, it becomes more easy to see how a margin of error as small as +/-25 years is possible for many manuscripts.
To begin, let's put this into perspective by looking at a few manuscripts of the English language and how handwriting has changed over the years. (Note that you can find higher resolution copies at Wikipedia.)
Gettysburg Address (Hays copy) - 1863
Historically speaking, this is a fairly recent manuscript, written only 150 years ago. Aside from the individual style of this particular scribe, little differs from cursive writing of today. The loops on some of the taller letters are more prominent than modern writers may use, and crosses on the letter T extends horizontally in what would be considered stylized calligraphy today. Without knowing the date, one could easily confuse it with a document from as late as the mid 1900s.
US Constitution (original) - 1787
We've added nearly a century to history, now, and handwriting differences are becoming very apparent - even just from the appearance of the bold heading text. The "h" in "the" and the "l" in "People" have loops not found in modern writing. The "A" in "Article" is a combination of two angled lines, a horizontal underline, and a middle dot. One notable latter is the long "s", which no longer exists in our alphabet. It looks similar to a lowercase "f" with the line extending leftward. In modern English, pairs of "s" have replaced this, as in "blessing". This archaic handwriting orthography is a prominent enough change that the television show Futurama poked fun at it.
Magna Carta (exemplar copy) - 1215
Now, we are taking a leap nearly 800 years into the past. Not only has vocabulary considerably changed in that span of time, but handwriting has, as well. The most notable feature in this low-resolution image is that the lowercase letters are about 1/3 the height of the lines; whereas, modern writing will have them 50-60% of the height. Also, notice the deep leftward slant of the loops on certain letters, while others have no slant. At a quick glance, the script has an appearance similar to that of JRR Tolkien's Middle Earth lore, which pays homage to the time period of the Magna Carta.
Ancient Greek
Before the advent of paper, writing surfaces were rare, so scribes were rare. Thus, handwriting evolved at a much faster rate nearly 2000 years ago than it has in the past few hundred years. Though there will be disagreements between paleographers at times, most New Testament manuscripts can be dated to a window of +/-50 years, and some can be dated to +/-25 years.
We looked at English language manuscripts with known dates, so those documents would obviously not be the ones dated; they would, instead, serve as the references for dating other documents. Similarly, New Testament manuscripts would be compared to other manuscripts from the same geographical area that have known dates (legal documents, war letters, etc.) or known termina (relics from Pompeii, Dead Sea scrolls, etc.).
Re-Dating
With new papyrus and parchment manuscripts discovered every year, it is common for New Testament manuscripts to be re-dated. Generally, the initial dating is more conservative (i.e. later), and the manuscript will be re-dated older with more evidence. A consensus may or may not be reached by the paleography community for several decades.
P46 (a nearly complete Pauline epistle codex housed in Ann Arbor, Michigan, and Dublin, Ireland) was initially dated to around AD 225 +/-50, but the newest evidence places it around AD 150 +/-25.
P52 (a fragment of John 18 in Manchester, UK) was dated nearly 80 years ago to AD 125 +/-25. Never evidence further narrows the margin of error, but few paleographers have suggested additional dates.
The re-dating of manuscripts has had profound implications of the historical reliability of New Testament texts. Until as recently as a decade ago, less than 10 manuscripts were considered to be from the 2nd century AD. Now, combine all the newest archaeological discoveries with more accurate date determinations, and the 2nd century count is around 25 (covering about 60% of the total New Testament). There is also a good possibility that two new manuscript discoveries fall to the end of the 1st century AD, which would be within the lifetime of eye-witnesses to the events recorded.
By @HullBreach
