Every country & culture has its own rituals to pay respect to their ancestors. The time of the year when we pay homage to our ancestors according to Hindu culture is Pitru Paksha.
Pitru paksha is a fortnight that starts with the full moon and ends with the new moon in September/October. During this time, we pay respect and express gratitude to our forefathers (ancestors), and seek blessings from them.
Some rituals that are followed across Indian culture:
Offering food (Annadaanam):
Offering food to poor and needy and seeking their blessings. Offering food to your priests/gurus/teachers and seeking their blessings is considered auspicious. Vegetarian meals prepared without using onion or garlic are prepared and offered during annadaanam. Seasonal sweets like Kheer or Sandesh are distributed.
Tarpan
Water mixed with sesame seeds and flowers is offered while chanting mantras. The ritual is done facing south, invoking ancestors (Pitrs) up to three generations.
Fasting
Some eat only one meal per day and fast during Pitru paksha, as a sign of respect to their ancestors.
For those interested, but not sure how to go about it, sharing a few simple steps below.
Start with creating a family tree of your ancestors, naming 3 generations of your maternal and paternal ancestors. Add the names of those who belonged to your parents generation who have passed away in your families. Remember them during Pitru paksha and donate fruits, food or water to the poor during this period.