A GOOD QUESTION, submitted to Question, Science Times, of the New York Times:

Speaking in Tongues

By C. CLAIBORNE RAY
Published: January 30, 2007

Q. How do researchers know the pronunciation of the languages of long-gone peoples?

A. Scholars do not so much know the pronunciation of ancient languages as extrapolate and guess. They have had more success with some languages than with others, said Emily Teeter, spokeswoman for the Oriental Institute of the University of Chicago, a major center for the study of the ancient Near East. For example, she said, Semitic languages like Babylonian and Akkadian are closely related to ancient Hebrew, providing solid clues about how the other ancient Semitic languages were vocalized.

[...]

Arabic is also very important for comparative Semitics. The answer continues with ancient Egyptian, drawing on the Rosetta Stone and Coptic.