I don't speak Italian, but I've heard that Italian is a phonetic language; that is, if you know how a word is spelled, then you know how it is supposed to be pronounced, and vice versa. That's assuming you have learned a few simple rules about how various letters and letter-combinations are pronounced.

I don't know, but I would guess the various dialects of Italian work the same way—that is, they change the spelling as necessary to indicate how each word is pronounced in each dialect, but they still follow rigid rules.

In addition, there might be some vowel shifts that are too subtle to be represented with spelling changes, but you might be able to ignore these without being too far wrong.

So what you probably need to do is (1) learn how to pronounce standard Italian, (2) get a reliable printed text written in Neapolitan, and (3) apply the rules you have learned to the text.

Look here: Italian alphabet and Italian phonology at Wikipedia. (That last article is disappointingly technical. Maybe you can find something easier.)

On second thought, maybe you can skip that article and go directly to this one, which looks easier: Neapolitan language (What? They call it a language instead of a dialect? Shows you how much I know!)

Also, look at the links at the bottom of those pages.

Don't take anything I have said as gospel, but I hope it's good enough to get you started.