There are many sources from which this information can be pieced together. For example, there are some "rhyming dictionaries" for poets, written during the Tang dynasty, that are one of the sources for pronunciation of Chinese at that time. There are textbooks from early medieval Spain that attempt to teach people how to speak "proper" Latin, and tell the reader NOT to pronounce certain words in such-and-such a "wrong" way; from this, historical linguists can reconstruct how the pronunciation of Latin was changing into "vulgar Latin" (which used those "wrong" pronunciations), which eventually developed into Spanish. There are also more technical methods in historical linguistics, associated with the "comparative method" of reconstructing parent languages from existing daughter languges, that can tell us about the pronunciation of those older languages from the systematic similarities and differences of known languages.