How the date is fixed
Pitru Paksha begins falls on the first day of the dark half of the lunar month Bhadrapada (Krishna Pratipada). The date is the day on which that tithi is running at aparahna, the afternoon. In the North Indian (purnimanta) calendar the same fortnight is counted in Ashwina.
About
Pitru Paksha is the dark half of Bhadrapada in amanta reckoning (Ashwina Krishna in purnimanta), in September or early October. It begins on Krishna Pratipada, the day after Bhadrapada Purnima, though some families start with the Purnima shraddha itself. Each family performs the shraddha on the tithi of the dark half that matches the tithi on which the ancestor died; the governing period is aparahna (afternoon), so the day whose afternoon carries that tithi is chosen. The fortnight closes on Sarva Pitru Amavasya, the shraddha for all ancestors, after which Sharad Navratri begins the next day.
How it is observed
Tarpana (water offerings) and pinda daan for ancestors on their death tithi, with meals offered to Brahmins and crows.