My father used to read that poem aloud.

Literal

Father [topic-は] that poem [object-を] voice [object-を] putting-out read thing [copula-です].

声を出して読む means 'to read aloud' — literally 'reading while putting out one's voice.' ~たものです is the polite form of ~たものだ, expressing nostalgic recollection of a past habit.