Snape had applied for the post of Defence Against the Dark Arts, but Dumbledore refused.
Severus Snape is hired by Dumbledore to teach Potions at Hogwarts
Date circa September, 1981
Location in Canon OP17
He later says that he took up the post on Voldemort's orders (HBP2), so it's almost certain he began teaching at the start of the school year.