Ancient wine was made of grapes and therefore similar to modern wine; a processed food, in other words. However, ancient wine tended to be quite strong and was therefore almost always diluted with water. Wine was also mixed with honey and spices to give it added flavour. As a starting point, refer to the entry for "Wine" in the Oxford Classical Dictionary (p. 1574 in the fourth edition from 2012). In her book Food in the Ancient World (2006), Joan Alcock writes that "Wine and water were mixed in a ratio of 1:3, 1:5, or 2:5 – that meant large quantities could be drunk" (p. 193), but I'm not quite sure what she bases those numbers on. Wine would be mixed with water to taste more than following a specific ratio.

Here's a useful overview about wine from Robet I. Curtis's monograph Ancient Food Technology (2001), which deals with food from the ancient world in general, but focuses on the situation in ancient Greece on pp. 294-295:

Panyasis, the fifth-century BC epic poet, says that wine was the "best gift of society the gods" (θεών πάρα δώρον άριστον). Greeks believed that drinking wine in moderation and in diluted form distinguished them from barbarians. They also saw vineyards as symbolic of the good life and of the city-state at peace. The chorus of Attic farmers in Aristophanes' Pax (308), for example, addresses the goddess Peace as "most loving of the vine" (θιλαμπελώτατη), and at line 520 Aristophanes has Trygaeus ("Vintage" or "Harvest"), a Greek farmer, greet Peace with the appellation "O Giver of Grapes" (ώ πότνια βοτρυόδωρε). This drink was for Classical Greeks a basic food item, not a luxury consumed almost exclusively by the upper classes, as in Egypt, Mesopotamia, and the Bronze Age Aegean.

With respect to the Bronze Age Aegean, note this highly entertaining lecture from 2017 on "social drinking" by Jeremy B. Rutter (the PDF includes the full text, references, and the PowerPoint).

As Curtis writes, drinking undiluted wine was considered the mark of barbarians. With barbarians, the ancient Greeks initially meant people who didn't speak Greek; later, the Romans adopted the word to refer to essentially anyone from outside of the Roman Empire, especially those were not Roman citizens (cf. Ammianus Marcellinus 15.12 about Gauls drinking undiluted wine).

The Greeks made use of a specific vessel for the mixing of water and wine, the krater. Sometimes, a psykter, another type of vessel, was filled with cold water (or even snow) and put in the krater to cool the wine. Wine was a key element in the Greek symposium (lit. "drinking together"), a typically elite way of consuming wine (among other things) and reinforcing social connections. Kraters and psykters, as well as jugs and cups used in the symposium, were usually of high quality (e.g. Attic black- and red-figure ware).

Tsipouro (and ouzo) postdate antiquity.