OK, Nick wading in.
Like James Garry and Robert Todd said: the digamma, ϝ, is an archaic letter of Greek, pronounced as /w/. It is present as a sound in Linear B, and it survived into Aeolic, but it did not survive into the other *written* dialects of Greek.
We know it was there in Ancient Greek for three reasons.
- First, Indo-European reconstruction. Like James said, we know that οἶνος oinos used to be ϝοῖνος woinos, from other Indo-European languages preserving a related sound; e.g. Latin vinum.
- Second, internal reconstruction. In particular, syllabic augment of vowels. The past tense of ἔργω ergō “I work” should be *ἦργον ērgon, with an eta [ɛːrɡon]. It is instead εἶργον eirgon, with an ei [eːrɡon]. That makes no sense, until you realise (a) that Attic ei corresponds to Homeric ἔεργον eergon [eerɡon], and (b) that happens because there used to be a /w/ there: ἔ-ϝεργον ewergon. So it’s just an epsilon prefixed to a consonant, like all other syllabic augments
- Why yes, *wergō is cognate with English work.
- Linear B is not an argument for working out where digammas were, because that’s circular: we were able to decipher Linear B based on the external and internal reconstruction of Greek.
- The final criterion is hiatus in Homer, gaps between vowels in the metre that do not make sense by how Greek verse is supposed to work. They do make sense, if we posit that there used to be digammas there in the original verse.
There is a delightful Xena fanfic about the digamma: For Ant of a Nail
So digammas are not written down in Homer, but we know they were there. They were only written down in Aeolic and Linear B.
Ioannis Stratakis (podium-arts.com) is meticulous in his reconstruction; I also hear digammas in his Herodotus. ἴδεν, he pronounces as ϝίδεν; we have evidence for that both from Latin, and from internal reconstruction (the augmented aorist is εἶδεν, with a syllabic augment).
ἄστυ – Wiktionary tells me that ἄστυ used to have a digamma too:
From ϝάστυ (wástu), with possible connection with Sanskrit वस्तु (vastu, “house”) and Latin verna.