Linguists are confident in having a good reconstruction of which Middle Chinese sounded like. The evidence for the pronunciation of Middle Chinese comes from several sources: modern dialect variations, rhyming dictionaries, and foreign translations.
Just as Proto-Indo-European can be reconstructed from modern Indo-European languages, so can Middle Chinese be reconstructed (very tentatively) from modern dialects. In addition, ancient Chinese philologists devoted great amount of effort in summarizing the Chinese phonetic system through "rhyming tables", and these tables serve as a basis for the work of modern linguists. Finally, Chinese phonetic translations of foreign words often provide clues. For example, "Dravida" was translated by religious scribes into a series of characters 達羅毗荼 that are now read in Mandarin Chinese as /ta35 lwo35 phi35 thu35/. This suggests that Mandarin] /wo/ is the modern reflexes of an ancient /a/-like sound, and that the Mandarin tone /35/ is a reflex of ancient voiced consonants. Both of these can in fact be confirmed through comparison among modern Chinese dialects.
See also: Chinese language