How the date is fixed
Every new-moon day, taken as the day on which Amavasya is running at sunrise. One that falls on a Monday is called Somvati, on a Tuesday Bhaumvati, and on a Saturday Shani Amavasya. Amavasya ends the dark half, so both month names are given.
About
Amavasya is the tithi in which the Moon's longitude returns to the Sun's, closing the dark half and, in amanta reckoning, the month itself. It is the tithi of the pitris, and tarpana for ancestors is its regular observance; the aparahna (afternoon) is the governing period for shraddha, so the day whose afternoon carries Amavasya is chosen. Several named Amavasyas stand out: Sarva Pitru Amavasya ending Pitru Paksha, Diwali on Ashwina Amavasya, Mauni Amavasya in Pausha, and any Amavasya on a Monday (Somvati) or Saturday (Shani). Solar eclipses can only occur on Amavasya, which is why eclipse rules are tied to it.
How it is observed
Tarpana for ancestors in the afternoon, river bathing on Somvati and Mauni Amavasya, and lamps at dusk.