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In Fruits Basket S2E5, around 20:30, Hanajima says something that sounds like "mochi atabou yo", which is subbed as "of course". I guess from this and her character that it's probably some archaic form of 勿論, but I've just started learning Japanese and don't really know how to look that up, besides searching for couple of ways I imagine it could be spelled (found nothing).
Can anyone tell me what it is she actually says?
How should I go about looking up something like this in general?
Most probably your transcription is correct: もちあたぼうよ
It is divided as
Regarding よ, I'm not really sure which definition applies, but it may be 語調を整えたり、強めたりする意を表す. Essentially it does not affect the meaning.
On your question of how, colloquial expressions are often not covered in Japanese-English dictionaries, so it may be necessary to consult decently large Japanese dictionaries.
