How do scholars date the ancient manuscripts and written records from the
past and are there methods accurate?

Scholars use a number of methods. You might think that carbon-14 dating,
which gives an objective date for when the papyrus or vellum or other
material was produced, would be the principal method, but actually it is
not. Carbon-14 isotopic dating requires the destruction of at least a
small portion of the manuscript material. Besides, it is only accurate to
plus or minus about fifty to one hundred years. For this reason, generally
more indirect methods of dating are used. Scholars compare styles of
paper, styles of script and other types of evidence from the manuscripts
themselves. For example, Greek texts changed over time from using all
capitals (uncial manuscripts) to having capitals and small letters. The
shapes of hand-printed letters tend to change with time. The types of
materials used for inks tended to change with time as well. In general,
scholars believe they can determine at least as precisely the date of a
manuscript from such evidence as with using carbon-14 dating, without
needing to destroy part of the manuscript.

About how precise the dates are, that is a good question. I would say that
if a number of scholars from different perspectives have studied a
document and all are tending to agree fairly closely on a date of writing,
you can be very confident. For example, the Rylands papyrus, a small
fragment of John which has been dated to about AD 125 has been studied
closely by a great number of scholars. For this reason you can probably
assume that this date is correct within perhaps twenty-five years or so. A
more recent manuscript of Mark known as the Magdalene manuscript has been
dated to around AD 68. This is a very exciting find, but it has not been
studied as carefully or by as many scholars, so I would advise caution
about the date of this very interesting manuscript.

John Oakes, PhD