How the date is fixed
Hanuman Jayanti falls on the full-moon day (Purnima) of the lunar month Chaitra. The date is the day on which that tithi is running at sunrise (the usual rule, called udaya tithi).
About
In North India, Maharashtra and Gujarat, Hanuman Jayanti is kept on Chaitra Purnima, the full moon that ends the first lunar month, in March or April. The tithi at sunrise is taken, and in Maharashtra the observance begins before dawn. Other regions use other dates: Tamil Nadu and Kerala keep it on Margashirsha Amavasya (Margazhi, Moola nakshatra), and Karnataka and Andhra on Vaishakha Krishna Dashami. The engine follows the northern Purnima rule and notes the regional alternatives.
How it is observed
Recitation of the Hanuman Chalisa and Sundara Kanda, and offerings of sindoor and laddoos at Hanuman temples.