Dhanteras falls two days before Diwali. Hindus consider Dhanteras an auspicious day to buy new things, such as gold, utensils or anything made of metal. Why?
Dhanvantri is considered the God of Ayurveda and the giver of good health. He emerged from the churning of the celestial ocean (Samudra Manthan), bearing a kalash (pot) full of amrit (nectar). This probably explains the link between metal and Dhanteras. Devi Lakshmi also emerged during the churning, and she is worshipped too.
Another story says that King Hima was destined to die of a snakebite on the night of Dhanteras. His devoted wife kept watch all night. She piled gold and silver at the entrance to his room to dazzle Yama, who came disguised as a snake. Her plan worked. That is why Yama is appeased on Dhanteras by buying metal.
Source: https://www.exoticindiaart.com/article/story-of-dhanteras

In some parts of the country, the lady of the house places diyas made of atta (wheat flour) or raw clay outside the house, facing south, on the night of Dhanteras or Choti Diwali. Other family members are not allowed to see the lamp. The diya burns all night to drive away evil spirits. The practice is linked to the story of King Hima, whose wife kept an all-night vigil to keep death away.
Interestingly, the first reference to Diwali is in the Kamasutra (2nd-3rd century CE), where it is called Yaksha-ratri, a festival celebrated on the full-moon night of Kartika with yagyas and gambling. Later writers like Hemachandra (11th century CE) clearly equated Yaksha-ratri with Diwali or Dipalika. Yakshas are celestial spirits who can be kind or harmful. The Yam ka diya is probably linked to this ancient practice.
Source: navbharatlive.com

Kukur Tihar, the festival of dogs, falls on the second day of Tihar, the country’s five-day Diwali celebration. Pets, strays and even police dogs are garlanded with marigolds, marked with a tika and fed their favourite treats. Nepalis consider dogs dear to Yama and believe that worshipping them pleases him.
People recall the story from the Mahabharata in which Yudhishthira refused to enter heaven in his earthly form without the dog that had faithfully followed him on his journey. That dog was Yama in disguise.

Bhaubij or Bhaidooj is also called Yama Dwitiya and is usually celebrated a day after Diwali. The practice of Bhaubij is mentioned in a 13th-century Marathi text called Lilacharitra, which describes how common people called Gosavis celebrated Diwali. It says that on Bhaubij, people cooked special dishes such as modak and laddoo.
Hemadri’s Chaturvarga Chintamani, a Sanskrit text from the same century, also describes the Bhaubij festival. It quotes a story from the Bhavishya Purana, which says that Yamuna (also called Yami) once hosted her brother Yama, the God of death, at her house. Since then, brothers and sisters have observed this festival.

Al Beruni came to India with the army of Mahmud of Ghazni. He wrote a famous book, Tehkeek-e-Hind (Discovery of India), in which he describes Diwali thus: “1st Karthika or new moon day, when the sun marches in Libra is called Diwali. Then people bathe, dress festively, make presents to each other of areca nuts & betel leaves; they ride to the temples to give alms and play merrily with each other till noon. In the night they light a great number of lamps in every place so that the air is perfectly clear.
The cause of the festival is that Laxmi, the wife of Vasudeva once a year on this day liberates Bali, the son of Virochana, who is the prisoner in the seventh earth. Therefore the festival is called Balirajya i.e. the principality of Bali.”
The day after Diwali is also called Bali Pratipada. Note also that Al Beruni’s description is very close to how Diwali is celebrated today.

Playing cards and gambling for small stakes are popular Diwali traditions. They are a symbolic ritual of luck. One of the most enduring motifs in Indian art is Shiva and Parvati playing a game of dice. Puranic tradition holds that the entire world was created through this divine play between Shiva and Parvati. They represent Purusha and Prakriti, and each move in the game mirrors a different state of the world, potential or realised. The dice game between Shiva and Parvati is shown in many sculptures, especially in Western India. Usually Shiva loses, but in a few rare reliefs he wins by cheating. In these, Parvati raises her hand in vismaya, or amazement. Vismaya is a key element in depictions of the Shiva–Parvati game.
Source: sahapedia.org

In most of South India, the main Diwali celebration takes place a day before the one in the North. It marks the killing of the demon Narakasura by Krishna and his wife Satyabhama, which is why it is called Naraka Chaturdashi. It is said that after their victory, they relaxed with an oil bath.
The eldest member of the family or the lady of the household puts three drops of sesame oil on the head of each family member before sunrise. The oil is then washed off with a mix of herbal powders or shikakai. The bath is called holy because it is considered as sacred as bathing in the Ganges.
Devi Mahalaxmi is said to have hidden behind a sesame plant, which is why sesame oil is used for the bath. Symbolically, the oil bath stands for a new beginning, washing away the ego. Sesame oil is also good for health and helps cool the body.

The day after Diwali also celebrates Krishna humbling the arrogant Indra. Indra had sent pounding rain and thunder to force the villagers of Gokul to worship him, and Krishna lifted the Govardhan mountain to shelter them.
The day is called Govardhan Puja, but it is also known by the more popular name Annakoot (thrashing of grains), which reflects its roots as a harvest festival. As part of the celebrations, a model of the Govardhan mountain is made from cow dung, and a variety of vegetarian dishes are cooked and offered to Krishna.

Rangoli, from the Sanskrit ranga-vali (line of colour), is the intricate floor art made with grain dust, powder, chalk or flowers at the threshold of homes during festivals. Some households draw rangolis with grain dust every day as a way to feed birds. During Diwali, the designs include Devi Lakshmi’s footprints to welcome her. Rangoli is first mentioned in the 2nd-3rd-century Kamasutra and then in the 6th-century Narada Shilpa Sastra. Later texts call it rangavali, dhuli-chitra (powder painting) or bhauma-citra (floor painting). The name rangoli probably became popular in Maharashtra, but other regions have their own names – Kolam (Tamil Nadu), Alpana (Bengal), Muggu (Andhra), Mandana (Rajasthan), Aripana (Bihar), Sathiya (Gujarat) and Chowkpurana (North India).
Source: https://www.britannica.com/art/rangoli

For many communities, Diwali marks the start of a new year in the Vikram Samvat calendar. It is believed that King Vikramaditya took the throne on Diwali and started a new calendar to mark the occasion. This calendar is 57 years ahead of the Gregorian calendar. During chopda pujan, the trading community closes its old account books and worships new ones for the new year, along with Ganesha, Lakshmi and Saraswati. The new account book is decorated with the words Shubh Labh (auspicious profit). The ritual is also called Sharda Pujan or Bahi Khata. Writing ‘Shubh Labh’ at the entrance of homes and puja rooms is now common across the country.
Source: https://www.diwalifestival.org/chopda-pujan.html

Stock markets open for an hour of symbolic trading on Diwali evening to bring good luck for the coming year. This modern take on chopda pujan began at the Bombay Stock Exchange in 1957 and was adopted by the National Stock Exchange in 1992.

Sri Chitragupta keeps a record of the karma of all beings and works with Yama, the lord of death, to deliver justice. Once, Yama complained to Brahma that he could not keep track of the karma of every single being. Brahma meditated, and Chitragupta was born holding an inkpot and pen (kalam dawat). Because he existed unseen (gupta) as an image (chitra) inside Brahma, he was called Chitragupta. Because he was born from Brahma’s body (kaya), he was called Kayastha. The scribal community of North India is known as the Kayasthas, and they worship the kalam-dawat on this day.
Source: https://glorioushinduism.com/2016/04/02/chitragupta/