Steps for Ammavasai Tarpanam
Prerequisites
1) Sit facing east direction
2) Collect the following items
one tambalam (fairly large to hold argyam),
panchapatram, udhirni, filled with potable water
raw rice - pachai arsi (25 gms),
black sesame seeds - karuppu yellu (50 gms),
dharbai (left most in image), pavitram (second from left in the image), koorcham (third from left in the image),
additional pottable water in a small pot, 
vetrilai pakku pazham (banana or apple or mango or any fruit that is available) 
& coins for dhakshinai
Detailed Steps
1) Aachamanyam
Take minute quantities of water(just sufficient to soak one grain of black gram) once for each mantra in the right hand and take it while reciting the following manthra.
1. Om Achyuthaya nama - ॐ अच्युथाय नमः
2. Om Ananthaya nama - ॐ अनन्ताय नमः
3. Om Govindaya nama - ॐ गोविन्दाय नमः
Om keshavaaya namaH - ॐ केशवाय नमः - Thumb to touch right cheek
Om naaraayaNaaya namaH - ॐ नारायनाय नमः - Thumb to touch left cheek
Om maadhavaaya namaH - ॐ माधवाय नमः - Ring finger to touch right eye
Om govindaaya namaH - ॐ गोविन्दाय नमः - Ring finger to touch left eye
Om vishhNave namaH - ॐ विष्णवे नमः - Index finger to touch right nostril
Om madhusuudanaaya namaH - ॐ मधुसूदनाय नमः - Index finger to touch left nostril
Om trivikramaaya namaH - ॐ त्रिविक्रमाय नमः - Little finger to touch right ear
Om vaamanaaya namaH - ॐ वामनाय नमः - Little finger to touch left ear
Om shriidharaaya namaH - ॐ श्रीधराय नमः - Middle finger to touch right shoulder
Om hR^ishhiikeshaaya namaH - ॐ ह्रीषीकेशाय नमः - Middle finger to touch left shoulder
Om padmanaabhaaya namaH - ॐ पद्मनाभाय नमः - Four fingers to touch navel
Om daamodaraaya namaH - ॐ दामोदराय नमः - Four fingers to touch head
This is a preliminary purification ceremony. The most auspicious divine names of the Lord, Achyutha, Anantha and Govinda are chanted and then chanting twelve other names of Vishnu purifies the self.
2) Wear the pavitram (second from left in the image below) on the ring finger on your right hand
3) Take three dharbai and place it under the feet. Recite the mantra
Dharbeshva seenaha - धरबेश्व सीनह:
4) Wash your hand with few drops of water. Recite the mantra
Apao pash pashya - अपाओ पश् पश्या
5) Take another three dharbai and place it along with your pavitram on your right hand. Recite the mantra
dharban dharyamaanaha - धरबन् धारयमानाह:
6) Ganesha Dhyanam: Recite the mantra
Shuklambaradharam Vishnum Sasi Varnam ChathurBhujam, Prasanna Vadanam Dyayeth Sarva Vigna Upa Santhaye
शुक्लाम्बरधरं विष्णुम ससि वर्णं चथुरभुजम, प्रसन्न वदनं ध्यायेथ सर्व विग्न उप शान्तये
7) Pranayamam: Close the left nostril with ring finger of right hand and exhale from right nostril slowly. Close the right nostril with thumb of right hand. Now, open the left nostril and inhale slowly while reciting the following
a) Om Bhoohu - ॐ भूहू
b) Om Bhuvaha - ॐ भुवह:
c) Om Suvaha - ॐ सुवाह:
d) Om Mahaha - ॐ महह:
e) Om Janaha - ॐ जनह:
f) Om Thapaha - ॐ थापह:
g) Ogum Sathyam - ओगुं सत्यम्
Afterwards, close the left nostril also as before, so that air is held inside the body and recite the following
h) Om Tatsa vithur varenyam - ॐ तत्स विथुर वरेण्यम्
Bargo devasya dhi mahi dhiyo yona prachodayath - बर्गो देवस्य धिमहि धियो योना प्रचोदयथ
Close the left nostril with ring finger of right hand and exhale from right nostril slowly While exhaling, recite mentally the following Mantra and Say Om while touching the right ear
i) Om Apa - ॐ आप ह:
j) Jyothj rasa - ज्योति रसह:
k) Amrutham brahma - अमृतं भ्रह्मा
l) Bhoorbuvasuvarom - भूर् भुवत्सु वरोम्
j) om om om - ॐॐॐ
8) Sankalpam: Place your hand as shown in the image on your right thigh and recite the mantra
Mamo partha samastha duritha kshaya dwara, Sri Parameshwara preethyartham- ममो पार्थः समस्थ दुरिथ क्षय द्वार:, श्री परमेश्वर प्रीथ्यर्थम्
Thadaiva lagnam sudhinam thadaiva - तदैव लग्नम् सुधिनं तधैव
Tara balam chandra balam thadaiva - तार बलम् चन्द्र बलम् तधैव
Vidya balam dhaiva balam thadaiva - विद्या बालान् दैव बलम् तधैव
Lakshmi Patheth Angriyugam smarami - लक्ष्मी पथेथ् आङ्गरियुगं स्मरामी
Apavithraha pavitrova sarva vastaan - अपवित्रहः पवित्रोवा सर्व वस्तान्
Gato piva yesmareth pundari kaksham - गतो पिव येस्मरेथ पुण्डरी कक्षम्
sabhahya abhyantarah suchihi maanasam vachikam papam - सभाह्यः अभ्यन्तरः सुचिहि मानसं वाचिकां पापम्
karmanam samuparchitam srirama smaraneneiva vapohati na samsayaha - कर्मणं समपर्चितं श्रीराम स्मरणनेनिव वापोहति न संसायह:
Sreerama rama rama thithir vishnuhu tada varaha nakshatram - श्रीराम राम राम थिथिर् विष्णुहु ताद वर: नक्षत्रम्
vishnu reva cha yogashca karanam chaiva sarvam vishnumayam - विष्णु रेवच योगाश्च करणं चैव सर्वं विष्णुमयम्
Jagath sri govinda govinda govinda - जगत श्री गोविन्द गोविन्द गोविन्द
Adhyashree bhagavathaha mahapurshashya - अध्याश्री भगवथह: महापुरुषश्य
Vishnoragnaya pravarthamanasya adhyabrahmanaha- विष्णोर् अग्न्या प्रवर्तमानस्य अध्यब्रह्मणह: