I tried searching for some information on the festivals on the subreddit and found pretty much nothing interesting
How many days did a festival have? What sort of activities happened within a festival? And were there multiple festivals for the same deity in the same year or was it an annual occurrence? How many festivals were the annually in a polis like Athens? (I'd also be interested to read some information on other poleis)
So this is a question that is very broad and so I am forced to give a relatively broad answer; what follows is mostly based on evidence from the Classical period, but it’s general enough to apply broadly to the entire ancient Greek period from let’s say the middle of the sixth century BC onwards. As far as our knowledge about festivals are concerned, the surviving evidence ensures that we are much better informed about Athenian festivals than those organized elsewhere, with the exception of the great Panhellenic festivals (i.e. the Panhellenic Games organized in Olympia, Delphi, Isthmia, and Nemea), which I assume you will know at least something about.
All festivals were organized to celebrate one or more deities, and for some deities (like Zeus) they did organize multiple festivals in their honour within the same year. Festivals could be big or small, organized on a Panhellenic level, on the level of a city-state or part of it, or even confined to a small village. Important festivals, like the Panhellenic Games, could attract visitors (pilgrims) from all over the Greek world, others were more regional affairs or limited just to the local populace. Some festivals were very specific to a certain place, like the Panathenaic celebrations in Athens (in honour of Athena, the city’s patron deity), whereas other festivals were celebrated in different places in the Greek world, like the Thesmophoria (in honour of Demeter).
Festivals were celebrated in different ways, but they usually included some form of a procession to a sanctuary (where a cult image of the celebrated deity or deities were kept), as well as various performances (singing hymns, dancing, engaging in athletic competitions, music and drama contests, and so on). It’s always good to remember that ancient Greek plays were created for festivals, and specifically that playwrights engaged in competition. Naturally, an integral part of festivals was the sacrifice of one or more animals on the altar within the sanctuary of the deity or deities in question. Male animals were, as a rule, sacrificed in honour of male deities, female animals for female deities. Parts of the sacrificial animals were burnt for the gods, while most of the edible parts were prepared for consumption by the community: such meals were often the only occasion for many people to consume meat.
Festivals were organized frequently, but not everyone celebrated the same festivals. Women, for example, were excluded from attending the Olympic Games (though that did not preclude them from sponsoring athletes!). Some festivals practiced the reverse, and excluded men: the aforementioned Thesmophoria, for example, were intended specifically for married women. Some of these festivals lasted only a day, others several days and even more than a week; the Thesmophoria lasted three days. The ancient Greeks, by the way, didn’t have a “week” like ours, and thus no weekend, and festivals may have been a convenient time to take a break, even though a lot of business would have continued as usual.
I think this will do for now. Some suggested reading: