Get W. Sidney Allen's slim text _Vox Graeca_. It goes over not only how Ancient Greek was pronounced but also how we know. The evidence includes explicit notes from grammarians and other writers, graffiti, borrowings, puns, and later forms of Greek. Allen also has another book _Vox Latina_ which does the same thing for Latin.
But I didn't ask about how we know the pronunciation. I asked about how we know how to say hello. There are any number of good reasons the word for olive oil might be attested in Greek. It's not so obvious why "hello" would be attested -- it's usually something you say, not something you write down.
This one seems tricky. English letters do not normally begin with "hello", or even with any synonymous phrase. Instead, they use forms that are specific to written letters.
A good question. The best, i.e. least likely to be unreliable, sources are: epistles as preserved by papyri; conversations as preserved in ancient drama (especially comedy); phrase-books that survive from ancient school curricula; funerary inscriptions that use everyday language; graffiti.
