She had nothing to do yesterday.

Literal

She [topic-は] yesterday, anything to-do-things [subject-が] did-not-exist.

何もすることがない ('have nothing to do') chains three pieces: 何も + negative covers 'nothing,' すること nominalizes 'doing' as 'a thing to do,' and がない negates the existence of any such thing. The whole construction reads compositionally — 'as for any thing-to-do, it doesn't exist.' Japanese routinely marks the existential negative this way (がない rather than something parallel to 'have no'), reflecting the language's preference for stating that something doesn't exist over saying someone lacks it.