How the date is fixed
Chaitra Navratri falls on the first day of the bright half of the lunar month Chaitra (Shukla Pratipada). The date is the day on which that tithi is running at sunrise (the usual rule, called udaya tithi).
About
Chaitra Navratri begins on Chaitra Shukla Pratipada and runs through the nine tithis to Navami, which is Ram Navami. It is the spring counterpart of the better-known Sharad Navratri and opens the lunar year in North India. The start day is the civil day whose sunrise carries Pratipada; the ghatasthapana (pot-installation) is done in the forenoon of that day, avoiding Chitra nakshatra and Vaidhriti yoga where possible. A kshaya or vriddhi tithi within the nine days can make the festival eight or ten days long.
How it is observed
Ghatasthapana on the first day, daily worship of the nine forms of Durga, and fasting through the nine days by many households.