She takes over as the Transfiguration teacher after Albus Dumbledore is promoted to Headmaster.
She started teaching 39 years before the December of 1995 [Y15], so it was 1956 [Y-24] on the official timeline (CS/DVD).
Minerva McGonagall begins teaching at Hogwarts
Date December, 1956
Location in Canon PA18
Type of Event Wizarding world