The body consists of five elements - Prithvi (earth), Jala (water), Agni (fire), Vayu (air) and Aakasha (ether).
At the time of death , the praana attains a new body called aathivaahika which consists of only three elements - fire,air and ether. This new body emerges out leaving behind the 'dead body' which is subjected to funeral rituals. This new body, at the end of the pindapradana rituals during the ten days after death ,converts into what is called a bhogadeha. The bhogadeha travels for 12 months following the movements of moon and attains the chandramandala where pitruloka exists.
All throughout these 12 months, its existence is in prethavastha or as a pretha.As a result of the sapindeekarana ritual performed at the end of 12 months (which at present is performed on the 12th day, however, it is like issuing a post dated cheque, its result reaches the atma only at the end of 12 months) the prethavastha is lost and the atma attains pitruloka. The pitruloka exists on the invisible side of the moon. On amavasya or new moon day, the moon comes exactly between the earth and sun.The sun-rays fall directly on this invisible half of moon called pitruloka. It is noon time there, time for lunch. One day of pitrus consists of 30 human days. By offering food to pitrus in the form of amavasya tarpanam which repeats every 30 days is like feeding them every day.In fact, the amavasya is also supposed to be obseved like the yearly sraadham in the annam - homam format. However, it has been simplified to suit the present day situation. The rishis must have thought, if we insist on the elaborate version, people will altogether stop doing it.
One becomes eligible to perform Amavasya tarpanam only after the demise of one's father. Even if mother is alive, he can perform.Every form of life, moving and non moving desires jala (water) from the hands of brahmin. The tarpana is also performed every day with just water as part of daily bath and brahmayajna. However, amavasya tarpana is performed using water mixed with til.
The three important requirements for tarpana are darbha,water and til. Darbha is considered as equal in purity to Agni and water. Devas reside on the tip of Darbha, middle portion is of manushyas and the base of pitrus. A pavitram worn during amavasya tarpanam should be made of 3 darbhas. Water is considered as praana, energy,essence of all plants, medicine, annam, amruta and somarasa. The oil or tailam in til(sesame seeds) can satisfy hunger and remove heat.If tarpanam is performed at home on sapthami / trayodashi tithis or Sunday/Tuesday/Friday or janmanakshatra, til should be mixed with akshata (rice). A silver or copper vessel should be used for tarpanam.
'Pitru' sabda means protector or ancestor in general. Pitrus belong to different classes. Pitrus of brahmins are called somapas, those of kshatriyas are called havirbhuks, those of vaisyas are called aajyapas and those of sudras, sukaalis. Their status also depends on how they have lived their life on earth. Those who have performed yajna become somapas, those who have performed only haviryaga (rituals where only rice is offered to Devas) beome barhishidas andthose who have not performed any yajna become agnishwathas.
The immediate three generations of pitrus - father , grandfather and great grandfather are called asrumukha pitrus and the three generations above them are called naandimukha piturs. The yearly sraadhham, amavasya tarpanam etc. are meant for the immediate three generations above called asrumukhas. "Naandi"performed as part of upanayanam etc. are meant for the naandimukha pitrus.
There is yet another group called kaarunika pitrus which includes friends and relatives.The lord of pitrus is yama. However the group of father exists in the from of vasus, that of grandfather exists in the form of rudras and that of greatgrandfather exists in the form of aadityas( sun).The vasus are eight in number, rudras eleven and aadityas twelve.The brahmin fed in pitrusthana during sraadham is nominated as vasu-rudra-aaditya swaroopee meaning of the form of vasu-rudra-aaditya.The second brahmin is of the form of viswedevah who are the protectosr and escorts to the pitrus during their journey to earth to take part in the sraadham.There are 96 sraadhas to be performed every year in addition to the tithi sraadha which is in fact the only one being observed these days.
There are still people who perform all the 96 sraadhaas at least in the form of tarpanam as in amavasya. These sraadhas are amavasya (12),Samkramana or the first day of the solar month(12),Manvanthara (14), Yugadi (4), Mahalaya (16), Vyathipatha (13),Vaidhruthi (13) and Ashtakanvashtaka (12). The details of these are available in standard panchangam.
See the huge gap between what is ordained in the sastras and what is in practice.