This excerpt is taken from Dr. Tariq Humayun Sheikh's book Eid ul-Adha.
The Method of Sacrifice by the Messenger of Allah ﷺ
❀ It is narrated from Umm al-Mu'minin Sayyida Aisha Siddiqah (may Allah be pleased with her) that the Messenger of Allah (peace be upon him) ordered that a ram be brought which had horns, black feet, black eyes, and a black chest and belly. When such an animal was presented, the Prophet (peace be upon him) said: "Aisha! Bring the knife." Then he said: "Sharpen it on a stone." I did so, then the Prophet (peace be upon him) took the knife, caught the ram, laid it down, slaughtered it, and prayed:
بِاسْمِ اللهِ، اَللَّهُمَّ تَقَبَّلْ مِنْ مُحَمَّدٍ وَآلِ مُحَمَّدٍ وَمِنْ أُمَّةِ مُحَمَّدٍ
"In the name of Allah, O Allah! Accept it on behalf of Muhammad, the family of Muhammad, and the nation of Muhammad."
Reference: (Sahih Muslim: 1966, 1967, 1965 Sunan Abu Dawood: 2792)
❀ It is narrated from Sayyiduna Anas (may Allah be pleased with him) that the Noble Prophet (peace be upon him) slaughtered two rams which had horns and were speckled. While slaughtering, the Prophet (peace be upon him) said Takbir and Bismillah بسم الله والله أكبر and placed his foot on their necks.
Reference: (Sahih Bukhari: 5565, 7399 Sunan Abu Dawood: 2794, Sunan Tirmidhi: 1494)
❀ Sayyiduna Jabir bin Abdullah (may Allah be pleased with both of them) is a narrator of this hadith. He says that the Noble Prophet (peace be upon him) slaughtered two rams on the day of sacrifice which had horns, were speckled, and were castrated. When the Prophet (peace be upon him) turned them towards the Qiblah, he recited this supplication:
إِنِّي وَجَّهْتُ وَجْهِيَ لِلَّذِي فَطَرَ السَّمَاوَاتِ وَالْأَرْضَ عَلَى مِلَّةِ إِبْرَاهِيمَ حَنِيفًا وَمَا أَنَا مِنَ الْمُشْرِكِينَ، إِنَّ صَلَاتِي وَنُسُكِي وَمَحْيَايَ وَمَمَاتِي لِلَّهِ رَبِّ الْعَالَمِينَ، لَا شَرِيكَ لَهُ وَبِذَلِكَ أُمِرْتُ وَأَنَا مِنَ الْمُسْلِمِينَ، اَللَّهُمَّ مِنْكَ وَلَكَ عَنْ مُحَمَّدٍ وَأُمَّتِهِ، بِسْمِ اللهِ وَاللهُ أَكْبَرُ
"I have turned my face towards the One Who created the heavens and the earth, and I am upon the religion of Ibrahim, upright, and I am not among the polytheists. Indeed, my prayer, my sacrifice, my living, and my dying are for Allah, the Lord of all the worlds, Who has no partner. I have been commanded, and I am among the Muslims who submit. O Allah! This (sacrifice) is from You and for You, so accept it on behalf of Muhammad and his nation. In the name of Allah, Allah is the Greatest." Then the Prophet (peace be upon him) slaughtered them.