Was the Bible was written in languages that are long dead and no longer in use? If so, how do we know that we have understood those languages correctly and that the current translations of the Bible we have is correct?
Hebrew Old Testament
The Hebrew language was never extinct. From the ninth century to the nineteenth century, Hebrew was not spoken extensively, but is used mostly in Jewish religious observance and by scholars studying the Old Testament. Hebrew has made an amazing return from near-extinction and is today the spoken language of the Jews after they returned to Israel in 1948.
Greek New Testament
The Greek New Testament was written in Koine Greek, which stopped being used in 4th century A.D. But it is not true that the language laid dead for a long time before the New Testament was translated into other languages.
Whenever a language stops being in currency, the Bible will be translated into another language that was in currency. (When Hebrew stopped being widely used, people wanted to have the Old Testament in a language they understand and that gave birth to the Greek translation of the Old Testament, called the Septuagint.) Through this process we know that the translations were always done when the people still understood the language from which it was translated.
Similarly for the New Testament, when Koine Greek was still in currency, it was already being translated into another language that was gaining prominence. At that time, Latin became a widely used language with the advancement of the Roman empire and so the first translation we have of the Greek New Testament was into Latin.
Parts, at least, of the Bible were available in a Latin version in Africa in the last quarter of the 2d century. In 180, the church of Scillium, near Carthage, possessed a copy (evidently in Latin) of Paul’s letters. Tertullian quotes extensively from the Latin scriptures and Cyprian, bishop of Carthage (249–257), uses a practically complete Latin Bible.
The translated versions of the Bible were also not preserved in dead form. As the Latin language changes so does the translation so that everybody reads the Bible in a current language. Just look at the English Bible. We no longer feel comfortable with the “thee” and “thou” of the KJV but prefer the more reader friendly NIV or even New KJV. Likewise the Latin translations would undergo such changes.
So when King James ordered the translation of the Bible into English, the translators did not just look at the NT manuscripts in a dead language but have the advantage of all the live translations.