Mahalaya Paksha
The fortnight of Krishna Paksha in Bhadrapada month is Mahalaya Paksha — the period set aside for ancestors. It ends with Mahalaya Amavasya, on which tarpana is offered to all ancestors regardless of whether their individual tithi is known.
What tarpana involves
Tarpana is the offering of water mixed with black sesame, made with the sacred thread worn over the right shoulder (apasavya) and facing south. It is offered to three generations of the paternal line, and in many traditions to the maternal line and to teachers as well.
It is a shorter rite than full shraddha — typically 45 minutes to an hour — and requires no cooked offerings, which makes it practical for families living away from their native place.
Other occasions for tarpana
Beyond Mahalaya, tarpana is offered on every Amavasya, on solar transitions (Sankranti), on eclipse days, and on the tithi of a parent's passing.
What to keep ready
Black sesame, darbha grass, a wide copper vessel, and the names and gotra of the ancestors. The karta bathes before the rite. No fasting is strictly required for tarpana alone, though many observe it.