With extremely strong accents and sometimes probably hardly intelligible, depending on which time and place they land in. One primary problem is that there was no "Ancient Greek" pronunciation. Greece was not a single country back then but consisted of many different regions and kingdoms, who frequently went to war with each other (which I always found rather ridiculous. Compare the Kingdom of Rhode Island going to war with the City State of New York).

So Greek was what is called a pluricentric language and had IIRC at least five major dialects (Attic, Ionic, East Greek, West Greek etc.). Of course these changed significantly over the centuries, too.

There is obviously a whole field of research into Ancient Greek phonology and they have various points of reference to determine possible pronunciation. There are also a number of surviving texts that do discuss pronunciation of some words.

However, to me the most interesting tidbit was always that they found out how to pronounce the letter "η" (which in modern Greek is similar to "ee" like "meet") when a fragment of an ancient comedy by Aristophanes was discovered in which a guy is about to be sacrificed by a priest (I think?) and the priest tells him to behave like a sheep (as a kind of proverbial "sacrificial lamb" I suppose) and imitate sheep noises (difficult to put in English but something like "baa").

This was rendered as "βῆ βῆ" in the fragment and because Greek sheep have not changed their accent over the millennia, we were able to get some insight in to how that must have sounded. ;-)