How the date is fixed
Ratha Saptami falls on the seventh day of the bright half of the lunar month Magha (Shukla Saptami). The date is the day on which that tithi is running at arunodaya, four ghatis (96 minutes) before sunrise.
About
Ratha Saptami is the seventh tithi of the bright half of Magha, in January or February, kept for Surya. The Puranas describe the Sun turning his chariot of seven horses northward on this day, which is why it is also called Surya Jayanti. The ritual bath is taken at arunodaya, the last four ghatis (96 minutes) before sunrise, so the day on which Saptami is running at that hour is chosen. In South India the bath is taken with arka leaves placed on the head, and temples take the deity out in a chariot procession.
How it is observed
A bath before sunrise, an offering of water (arghya) to the rising Sun, and a chariot drawn in kolam or rangoli at the doorway.