
This is a reissue of the second edition of a book on the pronunciation of Latin in Rome in the Golden Age. It has a section of supplementary notes which deal with subsequent developments in the subject. The author has also added an appendix on the names of the letters of the Latin alphabet.
W. Sidney Allen's old Vox Latina https://www.cambridge.org/core/books/vox-latina/0D460CEF06E5... is apparently still the standard starting reference for classical Latin pronunciation, at least for English-speakers. (Many nineteenth-century German philologists died to bring us this information, of course.) People such as Luke Ranieri on YouTube use a version of Allen's system, though a number of people including Ranieri claim that there should be five vowel qualities rather than the seven described by Allen https://www.youtube.com/watch?v=eH8E5RKq31I .
Note that if you want to speak Latin that's roughly faithful to how it was spoken up to (but not necessarily including) late antiquity, pronunciation is actually less important than quantity: basically, using clearly distinguishable short and long vowels in the right places (plus not running together double consonants in some places). I suppose it's similarly important to get the stress right, but at least that's generally agreed to be pretty easy. Classical Latin quantity feels weird and unnatural to English-speakers, and to Romance-language speakers, German-speakers ... : words often include one or two or three unstressed long vowels before getting to the stressed syllable, which might or might not itself have a long vowel. Even people who advocate for (classically-)correct quantity often don't consistently get it right.
(And yes, Allen also did publish a Vox Graeca https://www.cambridge.org/ie/universitypress/subjects/classi... , too, but be careful: the pronunciation of Ancient Greek is a question that might actually get you into a fistfight https://www.youtube.com/watch?v=BybLbHPU7Qc&list=PLQQL5IeNgc... .)
W. Sidney Allen wrote Vox Graeca[1] and Vox Latina which are well-known works which detail both what we know about pronunciation as well as explaining how we came to know these things. We surely don't know everything and scholarship evolves, but it is hardly like what you seem to be suggesting.
It is interesting to know about some of the sources: ancient grammarians wrote about pronunciation, people poked fun at how other people talked in letters, epigraphers sometimes made mistakes on the order of "could of".
[1] https://www.cambridge.org/us/universitypress/subjects/classi...
https://www.cambridge.org/core/books/vox-latina/0D460CEF06E5...
[Vox Latina](https://www.amazon.com/Vox-Latina-Guide-Pronunciation-Classi...) is a good resource for reconstructed classical pronunciation.
* descriptions of the sounds by the Roman grammarians
* wordplay, onomatopoeia, spelling errors in graffiti, etc.
* the way in which sounds from other languages (particularly Greek) were adapted into Latin
* the way in which sounds of Latin were adapted into other languages
* comparative reconstruction of the Romance languages
* evidence from metrical poetry, which provides particular clues about consonant and vowel length
A very readable book on is W. Sidney Allen's _Vox Latina_.
[edit: meant to reply to immediately following sister of this post.]
The best approximation we have is what's called the "restored" pronunciation. If you're interested in all the nuances the best book for this in my opinion is Vox Latina by Allen. Alternatively, just listen to anything by Evan der Miller on his YouTube channel: http://www.youtube.com/user/evan1965. His Latin pronunciation is the restored Classical and extremely good.
If you took Latin in Highschool and want to get back into it you should check out a book course called Lingua Latina per se Illustrata. It introduces Latin through Latin and also contains MP3 recordings for the first 31 chapters in first book, all in very good restored Latin pronunciation by the author Hans Ørberg. (there's a torrent of all the Lingua Latina resources)