One needs to do Tharpanam to satisfy one's ancestors. Tharpanam is done by offering water mixed with til (gingelly) As per Hindu belief, tharpanam is as important as any other worship procedure.
The regular tharpanam, also known as "Sarva Amavasai" , is done on all New Moon Days of every month. Apart from those Amavasya days, beginning of 4 months viz Mesha ( Chithrai Tamil New Year), Karkadakam (Tamil Aadi month),Thula ( Tamil Aippasi month) , Makara ( on set of “Thai month” in tamil) and during Solar and Lunar Eclipses, tharpanam should be performed. The Amavasya that falls on the Diwali month ( usually occurs on the Diwali Day or the next day) is considered very auspicious for performing Lakshmi Puja. There are two tharpanams one actually need to perform during Amavasya.The first one known as “Pitru Tharpanam “ is performed to get the blessings of ancestors. ie : Though one will have many ancestors, this tharpanam is addressed to three generations of deceased father, grand father and great grand father along with their wives ( deceased) in one's ( Paternal ) family and grandfather, great grandfather and great great grandfather along with their wives in one's maternal family.The other one, “Karunya Tharpanam” is perfomed for deceased uncles, aunts or cousins who are excluded in Pitru Tharpanam along with deceased pets, animals, friends…etc.