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I saw the phrase 烏有{うゆう}に帰{き}す, which means to "become nothing" as if turning to ashes. The word "烏有" means nothing, but its parts are 烏 (crow) and 有 (to be). How did 烏有 come to mean nothing?
When I consulted a dictionary (kotobank.jp), it said it means: 「烏(いずく)んぞ有らんや」. What does that mean? I'm not sure how to translate that. Also, is there a place where the word is first used?
As others have noted in the question comments, 烏有 read as uyū derives from Classical Chinese. Its origins there appear to be based on 烏 (not "crow" here, instead used phonetically in Middle Chinese as an interrogative and negative indefinite pronoun, as noted by snailboat and Derpius in the comments above) + 有 ("to have, to be") → "none-have, none-be" → "nothing".
Addressing the latter portion of your question, いずくんぞあらんや is provided as the kun'yomi or native Japanese reading of the Classical Chinese term 烏有. いずくんぞ again has no relation to the "crow" meaning of 烏, and あらんや implies the opposite of the "to have, to exist" meaning of 有, but the full kun'yomi is related to the Classical Chinese meaning of the full phrase.
いずくんぞ is a contraction. Walking it back:
いずくんぞ literally appears to mean "wheresoever". In practice, its meaning was closer to "why" (perhaps similar to archaic English "wherefore"). The term mainly appears in Classical Japanese, in the kundoku (native Japanese recitation) of kanbun (works written in [broadly speaking] Classical Chinese). いずくんぞ was used to introduce a supposition as part of a rhetorical question with an implied negative answer: "why would [you think X, it be X, etc.] (because actually that's not the case)." One usage example given in Shogakukan's Kokugo Dai Jiten is いずくんぞ知【し】らん: "why would [someone] know it (when they probably don't)."
あらんや is similarly a contraction.
In Classical Japanese, the -む + や construction was used in rhetorical questions where the answer is assumed to be "no", somewhat like the English construction "would it be X" with intonation used to indicate a meaning of "it isn't X".
Putting it back together then, いずくんぞあらんや ultimately parses out to "why would there be anything?", intending "there isn't anything" → "nothing".
