Shanivara Vrata (शनिवार व्रत), the Shanaishchara Vrata, is the Saturday vrata of Shani. In the Skanda Purana, as given in the Vratraj, Shani himself gives it to King Dasharatha. It is begun on a Saturday of Shravana and kept for thirty-three Saturdays; the udyapana is done on the Saturday after.
How to keep the vrata
On Saturday at dawn, clean the teeth with a twig and bathe with fragrant oil, then do the daily rites.
Go to a shami tree, or if there is none, an ashvattha. Worship Shani there with sandal, flowers, akshata, incense, a lamp, naivedya and tambula. On the first day an altar is made at the root of the ashvattha with a bow-shaped mandala and an iron image of Shani on a buffalo, two-armed, holding a staff and a noose.
Wind seven threads round the tree, and make seven namaskaras and seven pradakshinas. Recite the ten names of Shani and listen to this katha; Dasharatha's stotra may be read.
After the 33 Saturdays, on the Saturday after, close the vow with the udyapana: a gold shami tree (or ashvattha), an iron image of Shani with seven black cloths, 108 homa offerings with शं नो अग्निः, an offering of krisara (rice and sesame), a black milch cow with her calf, and seven Brahmanas honoured and fed with food mixed with sesame and urad; then eat with family.
When to eat
The Vratraj does not set a rule for the weekly Saturdays. At the udyapana, after the Brahmanas are fed with sesame and urad, the vrati eats with family.
The story of King Dasharatha and Shani, from the Skanda Purana
When Shani reached the end of Krittika, the astrologers told King Dasharatha that Shani would pierce Rohini (the Shakata-bheda), bringing a terrible famine of twelve years. Vasishtha said that even Brahma and Indra could not prevent it.
Dasharatha rode his divine chariot up to the sphere of the nakshatras, put Rohini behind him and stood before Shani with the samhara weapon drawn to his ear. Shani, pleased with his courage, offered a boon. Dasharatha asked that Shani never pierce Rohini while rivers, oceans, sun, moon and earth endure, and Shani agreed: there would be no twelve-year famine.
Dasharatha then praised Shani with his stotra. For a second boon he asked that Shani never afflict the three worlds; Shani agreed and told him how he should be worshipped, on the Saturdays of Shravana. Dasharatha worshipped him at Ayodhya and ruled the earth.