How the date is fixed
Vat Savitri falls on the new-moon day (Amavasya) that closes the lunar month Vaishakha. The date is the day on which that tithi is running at sunrise (the usual rule, called udaya tithi). In the North Indian (purnimanta) calendar the same fortnight is counted in Jyeshtha.
About
Vat Savitri recalls Savitri, who won back her husband Satyavan from Yama. In North India it is kept on Jyeshtha Amavasya of the purnimanta calendar, which in amanta terms is Vaishakha Krishna Amavasya, in late May or June. Maharashtra, Gujarat and parts of the south keep Vat Purnima instead, fifteen days later on Jyeshtha Purnima. The tithi at sunrise is taken for both; the engine lists the northern Amavasya rule and notes the Purnima variant.
How it is observed
Married women fast, tie thread around a banyan tree while circling it, and hear the Savitri story.