When it falls
Diwali falls on Amavasya (the new-moon night) of the Krishna Paksha in the lunar month of Kartik, usually in October or November — see our article on why Hindu festival dates change every year for how the lunar Panchang determines the exact date each year.
Which deity is worshipped
The main night of Diwali centres on Lakshmi puja, inviting the goddess of wealth and prosperity into a freshly cleaned, lit home — often alongside Ganesha, worshipped for wisdom and to remove obstacles at the start of any new venture, including the financial new year many households and businesses begin that night.
Why it's celebrated
Diwali's central story is Rama's return to Ayodhya after fourteen years of exile and his defeat of Ravana, as told in the Ramayana. Tradition holds that the people of Ayodhya lit rows of oil lamps (deepavali literally means "a row of lights") to welcome him home in the dark of the new-moon night — which is why light, quite literally, is the whole point of the festival. Diwali is also significant to Jains, who mark it as the day Mahavira attained moksha, and to Sikhs, who celebrate Bandi Chhor Divas alongside it.
How it's celebrated
Diwali isn't a single day but a five-day arc: Dhanteras opens the festival with the purchase of metal or gold, associated with prosperity; Naraka Chaturdashi (Choti Diwali) marks Krishna's defeat of the demon Narakasura; the main day centres on Lakshmi puja; Govardhan Puja the next day recalls Krishna lifting the Govardhan hill to shelter villagers from Indra's storm; and Bhai Dooj closes the festival celebrating the bond between brothers and sisters. In the days before, homes are deep-cleaned and decorated with rangoli; on the main night, diyas are lit throughout the house and courtyard, and the evening includes sweets shared between neighbours and family, gift-giving, and fireworks. Businesses commonly begin new account books (chopda pujan) on this day, treating it as a financial as well as spiritual new year.