I would not exactly say difficult, in most cases. We try to find the oldest possible primary poem source for whatever (like, say, using how Hades seems/acts in The Homeric Hymn To Demeter as a basis for characterization, and trying to only extrapolate a reasonable amount from stuff like that), and see how that fits.
Then also sometimes, if it can provide a more interesting result, we go into more archaeological detail, cross-referencing with what later writers say about things, and so on (such as books on prehistoric Crete). So there is some of the regular Greek pantheon based on poetry, some nods to the local gods of Crete based on archaeology (where almost no readable writing survives), and try to combine them in ways that seem interesting or like they reveal some striking idea. Or something like that.
It is more just a process than it is difficult. A long series of "Does that work? How does that feel? Does that mean anything?" in order to find something which fits and works and resonates, while trying to avoid as many received-through-pop-culture understandings of things as possible. The most difficult it gets is when I know I read something somewhere, but I cannot find the exact location of a quote. Haha.