Detailed rules about sacrificing animals
The animal should be watered and made to lie down on its flank so that its head is pointing towards the south and the muzzle in the direction of Makkah. Then one should take a sharp knife in the right hand and slit the throat just below the cartilaginous prominence (the “lump” in the throat) with the words “Bismillahi Wallahu Akbar.” This should be done with such force that the 2 carotid arteries, esophagus (food pipe) and the trachea (wind pipe) should be cut but the head should not be severed from the body.
Cutting these 4, viz. the esophagus, the trachea and the 2 jugulars is compulsory. As mentioned in Radd Ul Muhtaar, Vol. 5, Pg. No. 207.
It is Commendable (Mustahab) that the person on whose behalf the sacrifice is being performed should slaughter the animal himself/herself. If he/she cannot do so and someone else is doing so on their behalf, then it is better that he/she should be present at the time of slaughter. As mentioned in this Hadith:
It is narrated on the authority of Hadhrat Ali (May Allah be well pleased with him) that the Holy Prophet (Sallallahu alaihi wa sallam) told Hadhrat Fatima (May Allah be well pleased with her): O Fatima! Get up and stay with the animal that is being slaughtered on your behalf. Listen! With the first drop of blood that is shed, all the sins of the person on whose behalf the sacrifice is being performed are forgiven. Listen! On the Day of Judgment, the sacrificial animal will be brought with 70 times its blood and meat. Then, it will be placed in the balance (Mizaan). Hadhrat Abu Sa‘eed Khudri (May Allah be well pleased with him) said: O Prophet of Allah (Sallallahu alaihi wa sallam)! Is this especially for the Prophet’s Family? They are worthy of every benefaction that is particularized for them or is this for all? The Holy Prophet (Sallallahu alaihi wa sallam) said: It is especially for the progeny of Muhammad (Sallallahu alaihi wa sallam) and generally for all. (Kanz Ul Ummal, Hadith No. 12671)
What supplication to recite at the time of slaughter?
Supplications (Dua) to be recited at the time of slaughter
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
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.
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
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.
If at the time of slaughter, the animal jumps and one of its legs breaks or somehow it develops some other defect, then this defect does not affect the sacrifice. For e.g. if the animal jumps, develops a defect right at the time of slaughter and frees itself from the person/s handling it and is again recaptured, even then the sacrifice is valid. As mentioned in Radd Ul Muhtaar, Vol. 5, Pg. No. 229