Soorya Vrat

Soorya spoke - "Arun, One should always worship Soorya at Ayan time, Vishuv time, Sankraanti and Grahan time (Solar eclipse); especially on Saptamee. Saptamee is of seven types - (1) Ark-Samputikaa Saptamee, (2) Marich Saptamee, (3) Nimb Saptamee, (4) Phal Saptamee, (5) Anodanaa Saptamee, (6) Vijaya Saptamee, and (7) Kaamikaa Saptamee. One should start Saptamee fast from Maargsheersh or Maagh Shukla Saptamee, but for a grieved person there are no rules. Just before half an hour the night ends, one should clean his mouth, take bath and complete daily worship activities. Then do Jaap of enough Soorya Mantra. In the night sleep on floor. If somebody keeps fast drinking only 1/2 Anjulee (the shape formed by one hand to take something in it) water, it is called Udak Saptamee. It always gives pleasure.
[ Bhavishya, 1/22]

Soorya Vrat should be done on Saptamee or Ravi Vaar (Sundays). But there are some other Vrat also for Soorya.

"In Kaarttik Maas, everyday, worship Soorya Bhagavaan and feed a Braahman. One himself should also eat only once. By this method of worship all kinds of sins committed in childhood are destroyed. If one worships Soorya in Maargsheersh Maas in this way, he should donate Pannaa (emerald) to Braahman to destroy his sins committed in adulthood. If this Vrat (Ek-Bhukt - eating once a day only after sunset) is done in Paush Maas, all sins committed in old age are destroyed.

By doing this 3-month Vrat, people become the favorite of Soorya Bhagavaan. After first year, his small sins are destroyed, after the second year his medium class sins are destroyed, and after the third year even his greatest sins are destroyed and his desires are fulfilled. Thus this Vrat is completed in three months and one should do for three years. Whichever Vrat destroys the three kinds of sins - Adhi Bhautik, Adhi-Daivik and Adhyaatmik, is called Tri-Vikram Vrat."

Karaveer flowers, red sandal, Guggul Dhoop, Ghee lamp, and Modak (Laddoo) are Soorya's favorite. Teller of Puraan and Bhojak who worships me, both are dear to Soorya, that is why worship Braahman and listen to Puraan.
[ Bhavishya Puraan, 1/16]

Karaveer Vrat
Worship red Kaner flower tree in the morning to worship Soorya. Many Pativrataa women did this.
[Bhavishya Puraan, 4/5]

Soorya Shashthee Vrat - Year-long
One should do A-Yaachit fast today. Rishi eat in the morning, Pitar eat in the afternoon, Guhyak eat in the evening (Sandhyaa time), so a Soorya Vratee should eat only Sandhyaa time. One should start this vrat from Maargshersh Krishn Shashthee and follow it for 12 months with Soorya's different names. In the end feed Braahman Kheer and donate gold.
[Bhavishya Puraan, 1/20]

Ubhaya Saptamee
Keep fast on both Paush Saptamee, eat wheat flour food and milk, worship Soorya three times. Bathe Soorya with Ghee on 2nd Saptamee, offer Laddoo, cooked milk and food in Naivedya, and feed 8 Braahman.
[Bhavishya Puraan, 1/20]

Worship of Soorya in 12 Maas
[Bhavishya Puraan, 3/21  and   3/22]