How the date is fixed
Dattatreya Jayanti falls on the full-moon day (Purnima) of the lunar month Margashirsha. The date is the day on which that tithi is running at pradosh, the twilight just after sunset.
About
Dattatreya Jayanti falls on the full moon of Margashirsha, in December. The birth is placed at pradosh, so the day whose evening carries Purnima is chosen, and the birth ceremony is performed in that window. Dattatreya, the combined form of Brahma, Vishnu and Shiva born to Atri and Anasuya, is the central figure of the Datta tradition of Maharashtra and the Deccan. Gangapur, Narsobawadi and Audumbar hold their main gatherings on this day, and the Gurucharitra is read in the week before.
How it is observed
The birth ceremony at dusk, Gurucharitra reading in the preceding week, and bhajan at Datta shrines.