There are probably as many varieties of naturalism as there are naturalists. Either despite or because of this variety, many philosophers today are naturalists (though noteworthy dissent also exists). Philosophers of science, in particular, seem to be uncompromising naturalists. Here is one slogan that I think does a decent job of expressing the basic naturalistic position in a minimal enough form that most naturalists would accept it:
For any question, approach and answer that question the way a scientist would approach and answer that question (leaving the particulars open at this level of abstraction).
In other words, philosophers should defer to scientists on both questions of both method and factual content.
Another tenet of many modern naturalisms is "science is continuous with philosophy," a phrase which traces back to Quine. There is certainly something right about this notion, for we can point to current thinkers whose work does not fall neatly into science or philosophy: the late, great Rob Clifton is a paradigmatic example, as well as many other technical philosophers of physics working today. There are similar cases in other sciences too: should Sober and Wilson's Unto Others be classed as biology or philosophy?
However, it seems to me that "Science is continuous with philosophy" is also in some tension with the original naturalist slogan. If you asked an interdisciplinary team of scientists to answer the questions:
"Am I a brain in a vat (or being deceived by an evil demon, etc.)?"
"Is knowledge justified true belief?"
"Is the meaning of a sentence identical with its truth-condition?"
"Is the fundamental aim of science truth or empirical adequacy?"
they would (I think) say that such questions are not scientifically tractable -- in such cases, the 'scientific approach' (whatever exactly that might be) cannot answer that question. I think this would be the scientists' answer on the grounds that none of these questions -- or the vast majority of the others that appear in The Journal of Philosophy, Nous, The Philosophical Review, etc. -- are ever addressed in Science, Nature or other leading scientific journals.
In short: scientists do not view science and philosophy as continuous (even though there are borderline cases in technical philosophy of the special sciences), so a philosopher who views them as continuous is not fulfilling the naturalist's commitment to defer to the sciences. (Though the first stirrings of this discontinuity were felt earlier in the 17th C., I would guess that it becomes explicit with Newton and his rules of philosophizing.) So what is a philosopher (who is not Rob Clifton) to do? I think part of the appeal of naturalism is that science is seen as epistemically privileged, and if we can lump philosophy in with science, then that epistemic privilege and prestige will rub off on philosophy. I think the moral to be drawn from the discontinuity is just that philosophy lacks science's epistemological privilege -- and that is a conclusion a naturalistically-inclined philosopher might happily accept anyway.