Damodara Vrata, also called Kartika Vrata, is observed in the month of Kartika (October – November).
Suta Goswami says: If anyone fasts and observes the Kartika Vrata according to the rules and regulations, the Yamadutas (the messengers of Yamaraja) run away from him. The performance of Kartika Vrata is better than performing one hundred great sacrifices as prescribed in Vedic scriptures (Padma Purana).
How to observe Damodara Vrata?
Wake up early in the morning and take a bath. In Padma Purana, it is mentioned: “One who bathes early in the morning during the month of Kartika attains the merit of bathing in all places of pilgrimage.”
Chant at least one mala of Hare Krishna maha-mantra.
You can optionally observe a fasting vow during this month. Gaudiya Vaishnavas fast from Urad dal for the whole month of Kartika. In Skanda Purana, Lord Brahma informs Narada Maharishi: “One should follow Kartika fast and listen to narrations of Lord Sri Hari.”
Read the 9th and 10th chapters of the book Krishna, the Supreme Personality of Godhead authored by His Divine Grace A.C Bhaktivedanta Swami Srila Prabhupada which speaks about the pastime of Damodara in detail. A shorter version is available here.
Cook varieties of vegetarian food stuffs and offer to Lord Damodara. There are certain ingredients, which are prohibited and cannot be offered to the Lord.
Perform Damodara-arati. You can sing the Damodara-ashtaka and offer a ghee lamp to Lord Damodara. In Padma Purana, it is mentioned: Anyone who offers a ghee lamp to Lord Damodara in the month of Kartika will be freed from all kinds of sins and he goes to the abode of Lord Hari.
Alternatively, you can also offer a ghee lamp to Tulasi-devi and pray for eternal service at the lotus feet of Radha and Krishna in Vrindavana.
You may also invite your neighbors, relatives and friends to participate in this sacred Damodara Arati and give them an opportunity to offer ghee lamps to Lord Damodara & accept the prasadam of the Lord.