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She spends as much money as she earns.
Literal
She [topic-は] earn [nominalizer-の] [with-と] same amount money [object-を] uses.
稼ぐのと同じだけ stitches together three pieces. 稼ぐの nominalizes the verb — 'the act of earning, what she earns.' と is the と of comparison/equivalence ('the same as'). 同じだけ literally 'the same extent,' giving the whole phrase 'as much as she earns.' The result is the standard Japanese way to express quantitative equivalence between two amounts: 'X と同じだけ Y' = 'as much Y as X.' A neat construction worth committing to memory, with applications well beyond money.