My father often used to tell us about his student days.
Literal
Father [topic-は] often student-era things [object-を] us [to-に] told thing [copula-だ].
Another ~たものだ expressing nostalgic recollection. 学生時代 ('student era/days') is a common compound for referring to one's time as a student. ~のこと nominalizes: 'the things/matters of X.'