Slaughter the animal saying Bismallahi Wallahu Akbar and recite any of the Dua mentioned in the Hadith. There is a Hadith in Mo’jam Kabeer Tabarani about this:
It is narrated on the authority of Hadhrat Abdullah Bin Abbas (May Allah be well pleased with them) that the Holy Prophet (Sallallahu alaihi wa sallam) would slaughter 2 black and white sheep. When the Holy Prophet (Sallallahu alaihi wa sallam) would slaughter them, He would place His foot on the flank of the animal and say:
Transliteration of Dua: Bismillahi Allahumma Minka Wa Laka Allahumma Taqabbal Min Muhammad
Translation: In the name of Allah Most High. O Allah! This is Your grant and for You. O Allah! This is on behalf of Muhammad (Sallallahu alaihi wa sallam)! Please accept this. (Mo’jam Kabeer Tabarani, Hadith No. 11166)
In the aforementioned supplication, in place of Min Muhammad, one should say Minnee
In Sunan Abu Dawood, the following supplication is mentioned:
Transliteration of Dua: Innee Wajjahtu Wajhiya Lilladhee Fataras Samawati Wal Arza ‘Ala Millati Ibraheema Haneefanw Wa Maa Ana Minal Mushrikeen. Inna Salaatee Wa Nusukee Wa Mahyaya Wa Mamaatee Lillahi Rabbil A’alameen. La Shareeka Lahu Wa Bi Zalika Umirtu Wa Ana Min Al Muslimeen. Allahumma Minka Wa Laka ‘An Muhammadin Wa Ummatihee Bismillahi Wallahu Akbar.
Translation: Verily, I am steadfast on the creed of Hadhrat Ibrahim (May peace be upon him) and have turned away my face from all other religions to the One who peerlessly created the heavens and the earth. I am not among those who associate partners with Allah Most High. Indeed my Salaat, my Haj, my sacrifice of an animal, my life and my death are for Allah Most High who is the sustainer of all worlds. He has no partner and this is what I have been ordered to do and I am from among the Muslims. O Allah! This is Your grant and for You. O Allah! Accept this on behalf of Hadhrat Muhammad (Sallallahu alaihi wa sallam) and His Ummah. In the name of Allah Most High and He is great. (Sunan Abu Dawood, Hadith No. 2797)
In this aforementioned supplication, in the place of “‘An Muhammadin Wa Ummatihi,” one should recite: “‘Annee”.
The following supplication is mentioned in Haashiya As Sindi ‘Ala Sunan Ibn Majah:
Transliteration of Dua: Taqabbal Minnee Kamaa Taqabbalta Min Ibraheema Khaleelika Wa Muhammadin Nabiyyik
Translation: O Allah! Accept my sacrifice in the same way that You accepted from Your friend Hadhrat Ibrahim (May peace be upon him) and Your Beloved Hadhrat Muhammad (Sallallahu alaihi wa sallam). (Haashiya As Sindi ‘Ala Sunan Majah)
This supplication is also recited:
Transliteration of Dua: Allahumma Taqabbal Hadhihil Azhiyata Minee Kamaa Taqabbalta Min Ibraheema Khaleelika Wa Min Muhammadin Nabiyyika Wa Habeebia Alaihimas Salaatu Was Salaam
Translation: O Allah! Accept this sacrifice of mine in the same way that You accepted from Your friend Hadhrat Ibrahim (May peace be upon him) and Your Beloved Hadhrat Muhammad (Sallallahu alaihi wa sallam).
If someone else apart from the person on whose behalf the animal is being sacrificed is slaughtering the animal, then instead of “Minnee,” they should say: Min and take the name of that person and his/her father’s name. Similarly that person should say: Taqabbal Min so and so Bin so and so. Similarly, instead of “‘Annee,” one should say: “‘An” and take the name of the person on whose behalf the animal is being sacrificed and his/her father’s name.