What is Amavasya Tharpanam or Pithru Tharpanam?
Pitra (Pithru) means your ancestors; Tharpanam means to satisfy or to please. So, Pitra (Pithru) Tharpanam means satisfying the ancestors. Rituals that are connected to satisfy your ancestors remove the curse on your family.
There are many spiritual debts that each one of us needs to pay every day. One of these is our daily debt to our departed ancestors known as Pitra (Pithru). To pay off this debt, what we need to do daily is the worship procedure known as Pitra Tharpanam or Pithru Tharpanam. This worship procedure is quite easy. You can do it in about 10 minutes or so. 
What you need to do Pitra Tharpanam?
1.     A mat to sit on preferably made of sacred Darbha grass (also known as Kusa grass). A wooden plank or clean cloth made of natural fibers such as cotton or wool can also be used as a mat.
2.     A clean plate made of wood, copper, brass or silver. Iron, Glass and stainless steel are not appropriate.
3.     Clean water in a wood, copper, brass or silver cup that is convenient to hold in your left hand. You may also want to have water in a separate bowl. Glass and stainless steel are not appropriate.
4.     Black sesame seeds (ellu in Tamil, till in Hindi). If you are male, use black sesame seeds. If you are female, use white sesame seeds.
5.     Darbha grass (also known as Kusa grass)
6.     Pavitram made of Darbha grass to be worn on the ring finger of the right hand. 
How to select the names of the ancestors for doing this Pitra Tharpanam or Pithru Tharpanam?
You must select 12 recently departed ancestors as per the family lineage given below.
1.     Select 3 ancestors, who are recently departed as per the details given below (Paternal Male lineage)
Paternal Grand Father
Paternal Great Grand Father
Nalla Thambi
2.     Select 3 ancestors, who are recently departed as per the details given below (Paternal Female lineage)
Paternal Grand Mother
Paternal Great Grand Mother
Name not known
3.     Select 3 ancestors, who are recently departed as per the details given below (Maternal Male Lineage).
Maternal Grand Father
Seetha Lakshmi
Mother’s Grand Father
Mother’s Great Grand Father
Name not known
4.     Select 3 ancestors, who are recently departed as per the details given below (Maternal Female Lineage).
Maternal Grand Mother
Mother’s Grand Mother
Name not unknown
Mother’s Great Grand Mother
Name not known
What is the method of doing these Pitra Tharpanams or Pithru Tharpanam by our self?
2.     Spread the mat and sit facing east.
3.     Pray to Lord Ganesha first and then to Lord Surya Narayana who is the Lord of the Pithru ancestral beings. Request them to bless the Tharpanam pooja that you are about to perform.
4.     Place the plate in front of you and arrange the Tharpanam grid (made of Darbha grass) as shown above. First place the 3 vertical strips of Darbha grass and then the 3 horizontal strips. Each line shown above should have a minimum of 3 Darbha grass strips. Since there are 6 lines in total, you need a minimum of 6 x 3 = 18 Darbha grass strips.
5.     Now you can see that there are 12 tips in total, 3 at the top, 3 at the bottom, 3 on the right and 3 on the left. The top 3 tips represent the 3 most recently departed male ancestors on the father's side. The bottom 3 tips represent the 3 most recently departed female ancestors on the father's side.The 3 tips on the right represent the 3 most recently departed male ancestors on the mother's side. The 3 tips on the left represent the 3 most recently departed female ancestors on the mother's side.
With all your heart, request exalted Pithru ancestral beings to be present in this Tharpanam grid and accept the humble offerings that you are about to give. Now you are ready to do the actual Tharpanam cerem

1.     Pitra Tharpanamis done only for departed beings, that is, those who are dead. Pitra Tharpanam is not done for those who are alive.

2.     If you don't know the name of an ancestor, that is fine. Just state the relationship alone and offer Tharpanam for that ancestor.
3.     If you know the gotra lineage of a person, say it just before you mention the relationship, e.g., Sri Vatsa Gotra great grandfather Muruga or Vadhoola Gotra friend Suresh in the examples above. If you do not know the gotra of the person or you do not know what gotra is, just ignore this step.
4.     For those who wear the sacred thread, change it to your right shoulder at the beginning of the Pitra Tharpanam ceremony and back to the left shoulder at the end of the ceremony. There are special mantras for this step. If you don't wear the sacred thread, ignore this step.
5.     Can also do Pitra Tharpanam for more than 12 departed ancestors.
6.     There are special mantras for each specific ancestor. These special mantras will have their special effect for sure.
7.     The Pitra Tharpanam has to be done at the Sunrise; some people follow the procedure of doing this around noon.
8.     The Pitra Tharpanams could be done in the comfort of your house. It is very wonderful to do in the designated temples or on the banks of sacred rivers. It gives very good results, if it is done at Pithru Moksha temples or sacred spots.
9.     Pithru Tharpanam or Pitra Tharpanam can be performed by the following peoples. Elder Son/ other Son/ Wife/ Daughter/ Second wife/ Son or daughter of the Second wife/ Son or boy born out of wedlock
How to do Pitra Tharpanam (Pithru Tharpanam)?
1.     Pray to Lord Ganesha to make these rituals to become successful.
2.     Hold on to Black Till/ Gingelly seeds in your right hand palm. Hold water vessel on your left hand. Pour water into the right hand palm and slowly tilt your right hand so that the black till seeds along with the water flows through the gap between the right hand thumb and right index finger and fall directly into the tip of the Darbha grass.  Repeat the process for 3 times. 
3.     Now move on to the 2-nd tip and do the Tharpanam 3 times on that tip. In this way, repeat this process for all 12 ancestors, i.e., on all 12 tips. 3 times per tip and a total of 12 tips would mean that you make a minimum of 36 Tharpanam offerings for your Pitra or Pithru ancestors each time you do Pitra Tharpanam.   
5.     When your Pitra Tharpanam is complete, remove the Pavitram from your ring finger, unroll it and place it on top of the Darbha grass used in the Tharpanam.
6.     Pray to Lord Siva and the exalted Pithru and prostrate yourself (full body namaskar) towards the southern direction 12 times. 

7.     Dispose off the sesame seeds, water and Darbha grass used in the ceremony respectfully by depositing them into a flowing river or ocean or a large pond or well. An alternate method is to separate the sesame seeds from the water, pour the water alone at the base of sacred trees and feed the sesame seeds to birds. The important thing here is that the sesame seeds should not sprout.

பித்ரு த?ஷம் ப??்?ுவது ?ப்ப?ி ? (PITHRU THARPANAM IN TAMIL)

1. ?ிழ?்?ு ?ல்லது  த?ற்?ு ந??்?ி ?மரவும்.
2. பித்தள? ?ல்லது ??ம்பு பாத்திரத்தில் தண்ண?ர் ??ுத்து ??ள்ளவும்/
3. ?ால? ?று மணி ?ளவில் ??ய்ய வ?ண்?ும்.
4. ??ம்பு, மனம் த?ய்ம?யா? ?ரு?்? வ?ண்?ும்.
5. மனதில் விநாய?ர? வண?்? வ?ண்?ும்.
6. பின்பு ?றந்த முன்ன?ர்?ள? மனதில் ?ன்பு?ன் தியானி?்? வ?ண்?ும்.
7. நம்மு??ய ?ுற??ள? மன்னித்து நாம் ?ளி?்?ும் தர்பணத்த? ?ற்று ??ள்ளும்மாறு வ?ண்?ி?்??ள்ளவும். 
8. வலது ?ள்ள?்??யில் ?ருப்பு ?ள்ளின? ??ுத்து ??ள்ளவும்.
9. பாத்திரத்தில் ?ருந்து ?ிறிய ?ளவு தண்ண?ர? ??து ??யினால் ?ரண்?ி ம?லம் ??ுத்து வலது ?ள்ள?்??யில் ?ரு?்?ும் ?ள்ளின் ம?து ?ற்ற வ?ண்?ும்.
10. வானத்த? ந??்?ி ?றந்த முன்ன?ர்?ள? ?ழ?த்து நாம் ???ு?்?ும் ?ந்த தர்பணத்த? ஏற்று ??ள்ளுமாறு வ?ண்?வ?ண்?ும்.
11. பின்பு தண்ண?ரு?ன் ?ள்ள ?ள்ளின? வலது ??யில் ?ள்ள ?ள்?ா?்?ி விரல் மற்றும் ப?ரிய விரல் ந?ுவில் விழும்ப?ி நமது ??யின? வலது ப?்?மா? ?ாய்?்? வ?ண்?ும்.
12. ?ிழ? விழும் தண்ண?ர்  மற்றும் ?ள் நமது ???்?ு ??ியில் வ?த்திரு?்?ும் தாம்பாளத்தில் விழும்மாறு பார்த்து ??ள்ள வ?ண்?ும்.
13. ?த? ம?ன்று முற? ??ய்ய வ?ண்?ும்.
14. பின்பு தாம்பாளத்தில் ?ள்ள ?ள் மற்றும் தண்ண?ர? ?ால் ப?ாத ??த்தில் ?ற்ற வ?ண்?ும். 
15. ?ருப்பு ?ள் முள? வி?ாதவாறு பார்த்து ??ள்ள வ?ண்?ும். மு?ிந்தவர? ??ும் தண்ண?ரில் ப??ுவது நல்லது. 
16. ப?ண்?ள் ??ய்தால் வ?ள்ள? ?ள் ?பய?? ப?ுத்த வ?ண்?ும்.
17. தர்ப்பணம் ??ய்து மு?ித்த பின்னர் ?ந்த ??த்தில் ?ிறிய மா?்??லம் ப??வும்.
18. ?து மு?ிந்த பின்னர் ?ாப்பி?லாம்.
மற்ற?ரு முற?:
19. தாம்பாளத்தில் ப?்?ரி?ி ?ாதம் ??ய்து  ?தன் ம?தும் ?ள்ள? ப??லாம்.
20. பின்பு ?ள்ள? ?ாதத்து?ன் ?லந்து ?ா?ம்/ப?ு மா?ுவிற்?ு ???ு?்?லாம்.
21. ப?ு மா?்?ிற்?ு வாழ??்?ாய், வ?ல்லம் ?லந்த ?ரி?ி, ??த்தி ??ர? மற்றும் ??்?ர? ப??்?ல் ???ு?்?லாம்.
22. ?த? தினந்த?றும் ??ய்வது நல்லது.
23. ?ல்ல? ?ன்றல் மாதம் முதல் நாள், ?மாவ?? மற்றும் முன்ன?ர் ?றந்த திதியின? ?ண?்?ி?்?ு மாதத்திற்?ு 3 முற?யாவது ??ய்ய வ?ண்?ும். 
?ுறிப்பு :
1. ?வர்?ில்வர், ?ரும்பு, பிளாஸ்?ி?், ?ண்ணா?ி மற்றும்  ப??்?ான் ?பய??்?ி?்? ???ாது.
2. மணி ??ித்து ?ும்பி? ???ாது.
3. ?ுத்தம் ?ல்லாமல் ??ய்ய ???ாது.
4. ?ன்பும் ?ண்ம?யான பா?மும் நம?்?ு முன்ன?ர்?ளின் ??ிய? விர?வில் ப?ற்று தரும்.