I've seen wine. And I've seen the sea. Neither of them look anything alike. One can be a light/dark blue, or green, and the other one is typically a dark red. How did the association between wine and the sea come about?
It was red wine. The familiar "wine-faced sea" formula is a compound of oinos, "wine", and ops "face". In Archaic period texts we find three colour terms associated with wine. They are:
αἶθοψ (12× Iliad, 10× Odyssey, 2× Works and Days) -- "shining, gleaming": this adjective can be used of bright things like torches, but seems to indicate shininess rather than a light colour. It is also used of smoke (glittering with sparks) and the mythical Aithiopes, who were black-skinned.
μέλας (3× Odyssey) -- "black, dark-coloured". This is specifically a colour term and refers to dark colours, ranging around dark red, brown, and black. (It is also a typical epithet for soil/earth.)
ἐρυθρός (7× Odyssey, 1× Hymn to Demeter, 1× Archilochos) -- "red".
No other colour terms get used; in particular, not chlōros "pale". Therefore wine was prototypically red wine.
There are no particularly compelling explanations of why the sea gets described as "wine-faced". Some potential explanations are to do with the colour of the Aegean Sea at particular times of day;^1 I find that a bit of a stretch. Another suggestion is that the phrase "wine-dark sea" is a traditional East Mediterranean poetic collocation also supposedly found in Hebrew tarshish (supposedly "a qaṭlîl formation of the denominative root trš derived from tîrôš, 'wine,' paralleling ḥaklîl, and meaning 'wine-red' or 'wine-dark'");^2 but that argument relies on oinops meaning "wine-dark", which is emphatically not what it means.
Personally I suspect that oinops is simply being treated as a metrical variant for aithops, both words meaning "shiny". In very early Greek the two words had slightly different metrical properties because of a lost consonant at the start of oinops (i.e. *wīnops). Admittedly this explanation would be a lot stronger if we had examples of both adjectives being used in a complementary fashion. I don't think it's any weaker than the competing explanations I've mentioned, though.
Notes
^1 Rutherford-Dyer, R. 1983. "Homer's wine-dark sea." Greece & Rome 30: 125-8.
^2 Gordon, C. H. 1978. "The wine-dark sea." Journal of Near Eastern Studies 37: 51-2.