Simultaneously a lot and not very much.

Between archaeology and literature we have quite a bit of information about where temples were, how they were designed, what temple statues looked like, the names of gods, the basic outlines of sacrificial rituals (and sometimes the rituals in detail), what kinds of things people sacrificed and when, and even some takes on personal beliefs and experiences. One big problem is that the word "Greek" covers several millennia and a huge amount of geography, none of which was ever homogenous. So, for example, the Athenian sacrificial calendars that have been discovered by archaeologists tell us a lot about what was going on in Athens and in the 5th century BCE, but we can't necessarily apply any of that information to any other place or time, at least not without caution. Inscriptions of sacred law (many of these are basically organizational charters) tell us a lot about the workings of specific temples and associations, but it's harder to put together for how long those rules were followed and how typical any given charter was, although of course there are patterns.

There are real limits to our information. Pausanias has a wealth of descriptions about all kinds of different practices, myths, temples, etc., but in a lot of cases he's our only source, so we can neither corroborate what he's saying nor get insider perspectives on it. Other literary sources, like Homer and Hesiod, tell us a lot about the gods but less about how people worshipped them, and of course are only applicable to their own time periods. We also have to be aware that authors don't always have all the information, and might be leaving things out, filling in gaps with their own suppositions, or representing things in ways that are compatible with their individual agendas. Physical remains like temples and votives are incredibly helpful for understanding the material details of sacrifice and piety, but are completely silent about a lot of other things. Imagine walking into a church with zero background on modern Christianity--you could learn a lot just from the way the building and its rooms are laid out and decorated, but you'd never know what an actual service looked and sounded like. The practice of archaeology has also, ironically and unfortunately, made it impossible to recover some things. Early archaeologists were all about restoring and preserving the grand examples of classical architecture, which has skewed the ways we think about ancient society and destroyed a lot of evidence for later periods in the process.

The relationship between myth and worship is also not nearly as straightforward as a lot of modern people assume. Robert Graves and his contemporaries, bless them, spent a lot of time theorizing lost prehistoric rituals that only survived as myths, and vice versa, but much of that work has been debunked or at least is now understood to be unreliable. Some worship did use myth very closely, notably the mysteries of Demeter and Kore at Eleusis and many Orphic/Dionysiac mysteries, and many festivals were an opportunity to tell stories about the gods, but it's not necessarily correct to attach the personalities of Greek mythology to the gods of Greek worship--they're related but somewhat separate phenomena. Not to mention that the lack of homogeneity extends just as much to mythology as it does to worship. We've received all of this stuff in curated and compiled units--that's not how it was experienced by everyday people in the ancient world.

We can generalize a few things, the main one being that worship was a completely integrated part of ancient culture. How, who, and when people worshipped was connected to their political and economic situations, their gender and age, their family structures, and even their professions. Families were the basic unit of culture, and household worship was an important part of everyone's day (and, frustratingly, often the least well attested for modern understanding). Most or even all civic action included the gods. The most important buildings in most cities were the major temples, and each city had its own main protective deities, not to mention all of the minor shrines and temples. One reason that Christians had such trouble in the second and third centuries CE is because they weren't just worshipping a different god--they were removing themselves from civic and often family life. For the very pious on either side, the two systems were totally incompatible.

With those things in mind, the sources. We can pretty much divide them into literary and archaeological, although, again, we need to recognize the limitations of both. Pausanias's travelogues are major sources for both myth and worship, as are historians like Herodotus. Fictive accounts, like Homer, Athenian plays, and Roman-period novels, can tell us a lot about the kinds of things an audience would find believable, entertaining, or edifying. Compilations of myth and legend like Hesiod and Ovid are of course incredibly valuable.

Archaeological sources are physical things like artistic representations, inscriptions about people or organizations, the layouts of buildings or cities, etc. These can also tell us a lot. For example, the difference between western and eastern iconography of Artemis is striking, and which one we find in a particular city, or how they're combined, can help us think about the cultural and political life of that city.

The best thing, of course, is if we can find a literary description that's corroborated by archaeology. Accounts of the worship of the healing god Asclepius help us make sense of hoards of anatomical votives that have been found at various sites--basically, clay or wood representations of the body parts that were healed or needed healing. A lot of times archaeology and literature don't quite line up or even contradict each other, though, and so we have to be careful with the ways that we use them to interpret each other. So much has been lost, both of material culture and of literature, and so much was never preserved, like what some individual person thought when they attended a sacrifice.