As far as I know, though I could easily be wrong, Slavs didn't have writing before Cyril and Methodius, so consequently much less is known about their mythology. So, what is known about it, and how did historians come to those conclusions? What books would you recommend to a layman as a starting point in research?
Quite frankly, we don't know very much at all about Slavic Mythology, and the few things we do know are mostly reconstructions, with some exceptions. Several things, mostly names and some rites, have been deduced from the Chrisitian writings of the time, however, these sources are very biased, and prone to make things uo to defame the Slavic pagans. Most things that come out of these writings that are considered factual are considered such inly because they have been cross-referenced. For the most part, our knowledge of the Slavic pagans comes from archeological digs and what we've deduced from these writings.
As for books on Slavic paganism (and by extension, Rodnovery, the reconstructionist branch of Slavic paganism), unfortunantly, unless you read either Polish, Russian, or Czech, you're practically s.o.l., as most books on the subject are in these languages, and reliable translations (or, indeed, translations at all) are difficult if neigh impossible to find (especially online).
A warning: If you're serious about research into Rodnovery/Slavic Paganism, you are sure to hear about a so-called Book of Veles. It is in your best interest to discard any and all information relating to and originating from this "book", as it is a hoax. Sadly, many Rodnovers consider the Book of Veles a reliable source. It's not. I can't emphasis this more. The same is true, should they come up, of the "Slavic Vedas".
Source: I'm a Rodnover, and have done extensive research on this, hooray for the life of a reconstructionist :p