How are ancient scriptures dated?

To know about accurate dating, you have to know how fakes are made: most commonly, modern materials are used to create facsimiles of ancient works. These are easily foiled by the practice of carbon dating, which measures specific amounts of carbon isotopes in a material, and works from known constants (decay rates, normal ratios at creation of a type of material, etc.) to place a materials age rather accurately in the vast scope of history. In the rare cases where fraudsters take old materials to create their "artifact" much dating is done by cultural context present in the writing. The symbols, spelling, and grammar the writer uses, and what events they refer to make up a large part of this cultural context. It's very difficult to fake these without studying for YEARS in order to learn the nuances of a language, and makes forging something realistic in an obscure field almost impossible.

Oral histories are almost impossible to date, save for which confirmed events they refer to, and which they do not.

Science has tools like radiometric dating for specific text fragments. But all of these are copies, so they don't tell when the original was written, or even in what language the original was written. Those with embedded historical references are easy: "In the third year of the reign of King Uzziah..."

We can place upper limits if a document is quoted or mentioned in another writing that we can date. It gets much harder when you go back before people paid attention to what we call recorded history. It's even worse when people use the same writing style for everyday events that they use for hearsay, myths, and legends. It is unreasonable to expect any accurate dating of their origin.

You can carbon date an actual text.

As for the scripture itself, you need to rely on cross-references and historical records, checking that they are consistent; if Josephus referred to the Septuagint (he might have - don't know) then the Septuagint is older than Josephus (it is). And so on.

A major difficult academic field. There is an uncertainty of centuries in the age of Genesis, and I would imagine the Gitas are even worse.

i think some of them are oral tradition which is passed down mouth to mouth. and somewhere in the story telling there might be a date or two. but there are many different ways people can date scriptures but i don't know them all. oral tradition is written down by the way by monks and stuff... genesis was written during the babylonian exile, so people could have related the writing to different things in history.