Here is an example of how the the pronunciation of a language has been reconstructed in the past:
Various scholars, such as Girolamo Aleandro (1480–1542) and Aldus Manutius (1449–1515) judged that the pronunciation of Latin in the Middle Ages had drifted from the original descriptions of ancient grammarians.
For example, Varro affirmed that in the word centum, the orthographic <n> is realised as the velar nasal [ŋ]. Based on this hint, Erasmus (1466–1536) established that the velar nasal [ŋ] would have made sense only if <c> (before front vowels) represented the velar sound /k/ (as in /’keŋtʊm/), not /s/ or / ʧ/ (as in the pronunciation of the Middle Ages).
Of course, the further back in time we go, the less precise Historical Linguistic accounts are.
Below is an example from Classical Antiquity:
The following is one of the few comments from the Cratylus by Plato (424/423 BC–348/347 BC), in this regard:
[…] Shall I tell you what I suspect to be the true explanation of this and several other words?—My belief is that they are of foreign origin. For the Hellenes, especially those who were under the dominion of the barbarians, often borrowed from them (Salus (ed.), 1969: 44).
He admits the possibility that Greek has been influenced by ancient foreign languages, but does not comment on this further. The designation Plato adopts for alien speakers – βάρβαροι (literally, “those who say ‘bar bar’”; hence, the word “barbarian”) – is probably indicative of the Greeks’ attitude towards foreign and past languages, and why they were not interested in researching this topic any further.
Salus, P. H. (1969) On Language: From Plato to Von Humbolt. New York: Holt, Rinehart and Winston.