Some of my readers may find it strange that I am devoting a blog post to such things. Some of my readers are academics and other people who are long since thoroughly familiar with everything I'm going to say here. However, some of my readers are in other fields, and only an academic who has not spent a lot of time discussing ancient literature and textual transmission with the general public, and who has not read a lot of stories about new finds of ancient manuscripts in the mainstream media, nor watched a lot of TV shows about those subjects, knows these things, while being unaware of how many people do not know them.
The date of a text is the date when a certain piece of writing was first written. The date of a manuscript of that text is the date when a particular copy of that piece of writing was made. The general public almost never seems to show any significant interest in ancient texts other than the texts of the Bible and other Jewish and Christian writings, and this post is for the general public, so let's explain this with reference to those texts.
The 27 books of the New Testament are far and away the most thoroughly-researched texts in Western civilization. (I don't say they're the most most thoroughly-researched in the world because I don't know enough about texts from other civilizations to say so. For all I know, the scope of knowledge and research of the Vedas, or of the Koran or of Buddhist or Confucian texts, may utterly dwarf that of Biblical studies. I simply don't know.) There are tens of thousands of manuscripts of the New Testament. Many of these manuscripts are from the 5th century or earlier.
There are no original copies of any of the texts of the New Testament. By the way, scholars of ancient literature refer to a original copy as an "autograph." There are no autographs of the New Testament, there are no autographs of the Old Testament, or, as far as I know, of any ancient texts which are referred to as "literary" texts, which means: texts meant for a public audience: not just poems and plays and novels but also works of history and philosophy, and religious works such as the Bible. Scholars refer to all of such works intended for a public audience as "literary," in order to distinguish them from private letters, shopping lists, contracts, instructions from a government official to a subordinate, reports from such subordinates to their superiors, etc. We happen to have autographs of every one of those "non-literary" kinds of ancient writing, mostly in the form of papyri discovered since the late 19th century, a great many of them from the garbage dumps outside the ancient town of Oxyrhynchus, Egypt, where about a million fragments of papyri with writing of some sort or other on them have been found. About 5000 of those fragments from Oxyrhynchus, both literary and non-literary, have been published so far.
So. Anyway. To get back to the main theme of this post: The date of a text, the date when those particular words were first put to writing in that particular order, is different from the age of a manuscript containing that text, and when it come to ancient literary texts, that is: texts meant for a public audience, including religious texts like the Bible, we have no autographs. We have copies made later. The date of a Biblical manuscript is always later than that of the text recorded on that manuscript.
For very many ancient literary texts, we have no manuscripts made within 1000 years of the original text. For ancient Latin, pre-Christian, so-called "pagan" Latin ("pagan" originated as a term of abuse applied to those pre-Christian people by Christian authors in the 4th century and maybe earlier), it is very rare to have any manuscripts older than AD 800, older than the foundation of Charlemagne's Empire. Charlemagne did a tremendous amount to revive education and preserve those "pagan" Latin texts.
In the case of the Bible, until the 19th century, the oldest-known manuscripts for the Greek New Testament were from the 12th century, and the oldest-known manuscripts for the Hebrew Old Testament -- I don't know. Sorry. Pretty sure they were 10th century or more recent, but I don't know.
Then, starting in the 19th century, great discoveries of Biblical manuscripts were made. First, manuscripts from the 4th century were found here and there between Alexandria and Sinai in monasteries and antiquities shops, including the tremendous Codex Sinaiticus, a nearly-complete 4th-century copy of the Greek New Testament along with the Greek translation of the Old Testament known as the Septuagint, discovered by Constantine von Tischendorf in pieces at Saint Catherine's Monastery at Sinai in Egypt beginning in the 1840's and gradually put together over a period of decades, and now in 4 different libraries, but most of it in the British Library.
Beginning in 1896, Bernard Grenfell and Arthur Hunt found the huge piles of pieces of papyri at Oxyrhynchus, which I mentioned above. Most of these pieces of papyri are just little scraps which were discovered and preserved not long before they were going to become dust. So in that respect they're completely different than the nearly-complete Bible contained in the Codex Sinaiticus. However, many of the Oxyrhynchus manuscripts are quite a bit older than the 4th century AD. Some are as old as the 3rd century BC. They contain literary texts as well as the non-literary items described above. And these literary manuscripts include scraps of the New Testament from as early as the 2nd century AD, copies made with decades of when the text was first written, quite possibly within the lifetime of the original authors, something otherwise unheard-of for ancient literary texts.
In the 20th and 21st centuries the Dead Sea Scrolls and the Nag Hammadi Library and other very old papyri and parchments containing biblical and apocryphal texts have been found and continue to be found, although so far there has not been another find as huge as that at Oxyrhynchus. In 1979 in Jerusalem two silver scrolls were found containing the Priestly Benediction ("May the Lord bless and keep you..." etc) from the Book of Numbers. The verses were etched into the scrolls before 600 BC.
Have I cleared anything up or just confused you worse? I hope this has helped. Be careful when you're reading news stories or watching TV shows about these sorts of things, because sometimes these stories and shows have mistakes, like saying "4th-century text" when they should say something like "4th-century manuscript of a 2nd-centiry text" or what have you.
So how do people figure out how old the texts are? The same way they figure out how old the manuscripts are: I don't know. That is to say: I know some of the criteria used, such as handwriting styles, which vary quite uniformly over time and place or origin, and things mentioned and not mentioned in the texts, and where the manuscripts are found, and carbon-14 analysis and multi-spectral analysis and many other things. And I know that the experts very often disagree about the date of a certain manuscript or of a certain text, but that usually these disagreements have to do with very small differences in age: a decade or two, or sometimes as much an entire century, in the age of a manuscript 2000 years old or older. But if you hand me a manuscript and need an expert opinion of how old it is, chances are the best I will be able to do is hand it right back and refer you to some actual experts. I do know some experts.