My father lectured me, saying I had smoked a cigarette.
Literal
Father [topic-は] tobacco [object-を] smoked [saying-といって], me [to-に] sermon [object-を] did.
~といって marks the stated reason: 'saying that / on the grounds that X.' お説教をする means 'to give a lecture/sermon' — the お is beautifying. The structure implies the father caught the speaker smoking and reprimanded them.