This is something of a methodological question, but I always find it difficult to think about the internal beliefs of folks from long ago. For the purposes of this question, let's just confine ourselves to the Roman Empire. It seems to me that we have to rely on two main sources: what little writings we have and the physical remains of the people in question.
The writings we have, while no doubt extremely useful, are also going to be from the upper echelons of society. This bias means that they often aren't terribly concerned with the subjective experience of the common people. It also means that the views they express -- about religion or whatever else -- don't really strike me as representative in any meaningful sense.
The physical finds do a bit better, but even here I worry. For instance, there are a lot of Church's in Venice today, but simply counting them would give a false impression of the dominance of Christianity. They are preserved as cultural monuments and tourist attractions as well as for spiritual reasons. The upshot being that I am hesitant to infer from the mere presence and prominence of temples any conclusions about religiosity of the common people.
So I guess my question is how exactly we go about drawing conclusions about the religiosity of people from long ago.
It's a big problem, and a hard question to answer in general, because the kinds of sources we have vary so much depending on the period in question.
This varies from your Roman focus, but there is a great essay by Gregory Schopen Called "Archaeology and Protestant Presuppositions in the Study of Indian Buddhism." In it Schopen describes how archaeological investigations of Buddhist monasteries consistently suggest early Buddhist monks doing things (like owning property), that later textual sources say that Buddhist monks are forbidden from doing. Unfortunately, archaeologists and historians have tended to trust the textual sources over the material evidence, either by coming up with convoluted explanations for spaces that seem clearly to have been store-rooms, or by arguing that these monks were behaving "irreligiously." Schopen argues that this is a mapping of a Protestant assumption that the "true" practice of a religion is contained in a canonical text. However, we don't really know that early Buddhist monks had this same relation to religious texts, the earliest existing versions of which date to hundreds of years after the monasteries in question were built.
I think its also worth noting that ideas about what is and isn't "religion" can be hard to translate across time periods. For example, in the present day we understand that believing in the literal existence of Adam and Eve is "religious," believing in Julius Caesar is "historical," and believing in ghosts is "superstitious." But these kinds of distinctions have not existed everywhere and at all times.
So, to return to your question about how historians know about the religiosity of people in the past-There are a lot of ways to know what people did as part of their religious practices, and for some time periods we have records (usually textual) of what they thought about these practices. I think having a mix of textual and material sources, preferably of a wide variety, is really important if you are trying to make assumptions about what large groups of people believed internally. Even then, I think this is an area where there is a an especially big danger of presentism, especially when you try and asky questions like "were ancient Romans/Indians/Mayans/etc more religious than we are today."